1. sum, difference, multiplication and division:
(1) multiplicity relation: it is reflected by the key words "how many times, how many times, how many times, what percentage, growth rate …".
(2) How much relationship: it is reflected by the key words "more, less, harmony, difference, lack, surplus ……".
Example 1. According to the statistics of the fifth census released by Xinhua News Agency on March 28th, 2000 1, as of 0: 00 on October 28th, 20001,the population with primary school education per 10,000 population in China was 3,5701,while 6,5701.
Analysis: The equivalence relation is:
Solution: Suppose that at the end of June, 1990, about X out of every 654.38+million people have primary school education.
Answer: Omit.
2. Equal product deformation problem:
"Equal area deformation" is based on the premise that the shape changes but the volume remains unchanged. The commonly used equivalence relation is:
(1) The shape area has changed, but the perimeter has not changed;
② Raw material volume = finished product volume.
Example 2. A cylindrical glass (filled with water) with a diameter of 90mm was poured into a cuboid iron box with a bottom area of 81mm. How much mm did the water in the glass drop? (Results are rounded)
Analysis: The equivalent relationship is: the volume of cylindrical glass = the volume of cuboid iron box.
The falling height is the height of the poured water.
Solution: let the water drop in the glass xmm.
Answer: Omit.
3. Labor deployment:
This kind of problem to find out the number of changes, common problems are:
(1) can be transferred in and out;
(2) Only the transfer-in did not turn out, the transfer-in part changed, and the rest remained unchanged;
(3) Only the transfer-out has not been transferred in, some of the transfers have changed, and the rest remain unchanged.
Example 3. There are 85 workers in the processing workshop of the machinery factory, each of whom processes 16 large gears or 10 small gears on average every day. It is known that two large gears and three small gears form a group. How many workers should be arranged to process the big and small gears separately to make the big and small gears processed every day just match?
Analysis: List method.
Number of people per person per day
Gear 16 x person 16x
Pinion 10 person
Equivalence relation: 2 times the number of pinion gears = 3 times the number of large gears.
Solution: We arrange X workers and X workers to process large and small gears respectively.
Answer: Omit.
4. Proportional distribution:
The general idea of this kind of problem is: let one of them be x and write the corresponding algebraic expression by using the known ratio.
Common equivalence relation: sum of parts = total.
Example 4. The ratio of three positive integers is 1: 2: 4, and their sum is 84, so what is the largest of these three numbers?
Solution: Let one part be X, then the three numbers are X, 2x and 4x respectively.
Analysis: equivalence relation: the sum of three numbers is 84.
Answer: Omit.
5. Numbers.
(1) Need to know the representation method of numbers: the hundredth digit of a three-digit number is A, the tenth digit is B, and the first digit is C (where A, B and C are integers, 1≤a≤9, 0≤b≤9, and 0≤c≤9), then this three-digit number is represented as: 65438.
(2) Some representations in the number problem: the relationship between two consecutive integers, the larger one is larger than the smaller one1; Even numbers are represented by 2N, and continuous even numbers are represented by 2n+2 or 2n-2; Odd numbers are represented by 2n+ 1 or 2n- 1.
Example 5. For two-digit numbers, one digit is twice as much as ten digits. If the tenth digit is reversed, the two digits obtained are 36 larger than the original two digits. Find the original two digits.
Equivalence relation: original two digits +36= new two digits after switching.
Solution: Let the number x on the ten digits, then the number on the one digit is 2x.
The solution of10× 2x+x = (10x+2x)+36 is x=4, 2x=8.
Answer: Omit.
6. Engineering problems:
Three quantities in engineering problems and their relationship are: total work = working efficiency × working time.
Often when the total workload is not given in the title, the total workload is set to 1.
Example 6. For a project, it takes 15 days for Party A to do it alone and 12 days for Party B to do it alone. Now that Party A and Party B have cooperated for three days, Party A has other tasks, and the remaining projects will be completed by Party B alone. How many days does it take Party B to complete all the projects?
The analysis assumes that the total project amount is 1, and the equivalent relationship is: a completed workload +B completed workload = total workload.
Solution: Assume that it takes X days for B to complete all projects, and the total workload is 1. From the meaning of the question, (115+12) × 3+x12 =1,solve this equation, 65438.
12+ 15+5x = 60 5x = 33∴x = 335 = 635
Answer: Omit.
7. Travel problems:
(1) Three basic quantities in the travel problem and their relationships: distance = speed × time.
(2) The basic types are
(1) meeting problems; (2) follow up the problem; Common ones are: running for opponents; Navigation problems; Circular runway problem.
(3) The key to solve this kind of problem is to grasp the time relationship or distance relationship between two objects, so that the problem can be solved as a whole. And often sketch to analyze and understand the trip problem.
Example 7. The distance between Station A and bilibili is 480 kilometers. The local train departs from Station A at a speed of 90km per hour, and the express train departs from bilibili at a speed of140km per hour.
(1) The local train starts first 1 hour, and the express train starts again. The two cars are driving in opposite directions. How many hours after the express train leaves, will the two cars meet?
(2) After two cars started at the same time and walked in opposite directions for several hours, the two cars were 600 kilometers apart?
(3) Two cars start at the same time, and the local train runs in the same direction behind the express train. How many hours later, the distance between the express train and the local train is 600 kilometers?
(4) Two cars leave in the same direction at the same time, and the express train is behind the local train. How many hours will the express catch up with the local train?
(5) After the local train 1 hour, the two cars are driving in the same direction, and the express train is behind the local train. How many hours after the express train leaves, will it catch up with the local train?
The key to this problem is to understand the meaning of opposite direction, opposite direction and same direction, and to understand the driving process. So it can be combined with graphic analysis.
(1) parsing: When encountering a problem, draw it as:
The equivalent relationship is: distance traveled by local train+distance traveled by express train = 480km.
Solution: Suppose that two cars meet after the express train leaves X hours. From the meaning of the title, 140x+90(x+ 1)=480.
To solve this equation, 230x=390.
∴ x= 1 1623
A: A little.
Analysis: run in reverse, and the drawing is expressed as:
The equivalent relationship is: distance traveled by two cars +480 km =600 km.
Solution: suppose that after x hours, the two cars are 600 kilometers apart.
Judging from the meaning of the question, (140+90)x+480=600 solves this equation, and 230x= 120.
∴ x= 1223
Answer: Omit.
(3) Analysis: The equivalent relationship is: the distance traveled by the express train-the distance traveled by the local train +480km = 600km.
Solution: Let the distance between two cars be 600 kilometers after X hours. From the meaning of the question, (140-90) x+480 = 600 50x =120.
∴ x=2.4
Answer: Omit.
Analysis: Trace back the problem and draw it as follows:
The equivalent relationship is: express distance = local distance+480km.
Solution: Set the express train to catch up with the local train after X hours.
From the meaning of the title, 140x=90x+480.
To solve this equation, 50x=480∴ x=9.6.
Answer: Omit.
Analysis: Tracing back to the source, the equivalent relationship is: express distance = local distance +480 km.
Solution: Set the express train to catch up with the local train after X hours. From the meaning of the title, 140x=90(x+ 1)+480.
50x=570，x= 1 1.4。
Answer: Omit.
8. profit and loss problem
(1) The quantities that often appear in sales problems are: purchase price, sale price, bid price, profit, etc.
(2) Relationship:
Commodity profit = commodity price-commodity purchase price = commodity price × discount rate-commodity purchase price
Commodity profit rate = commodity profit/commodity purchase price
Commodity price = commodity price × discount rate
Example 8. A store will increase the purchase price of a certain clothing by 40%, then price it and sell it at a 20% discount. As a result, each piece of clothing still earned 15 yuan. What is the purchase price of each piece of clothing?
Analysis: It is the key to explore the implied conditions in the topic, and the cost can be directly set to X yuan.
Purchase discount rate, bid price, preferential price and profit
Twenty percent off (1+40%) X twenty percent off (1+40%) X 15.
Equivalence relationship: (profit = discount price-purchase price) discount price-purchase price = 15.
Solution: Let the purchase price be X yuan, 80% x (1+40%)-x = 15, X= 125.
Answer: Omit.
9. Savings problem
(1) The money deposited by the customer in the bank is called the principal, and the reward paid by the bank to the customer is called interest. Principal and interest are collectively referred to as the sum of principal and interest, the time of deposit in the bank is called the number of periods, and the ratio of interest to principal is called the interest rate. Interest tax is paid at 20% of interest.
(2) Interest = principal × interest rate × number of periods
Sum of principal and interest = principal+interest
Interest tax = interest × tax rate (20%)
Example 9. A classmate deposited 250 yuan in the bank for half a year. After half a year, * * * got the principal and interest and 252.7 yuan. What is the annual interest rate of the bank for half a year? (excluding interest tax)
Analysis: equivalence relation: sum of principal and interest = principal ×( 1+ interest rate)
Solution: let the real interest rate for half a year be x,
250( 1+x)=252.7，
x=0.0 108
So the annual interest rate is 0.0 108×2=0.02 16.
Improving the examination questions of one-dimensional linear equation
I. Comprehensive questions (6 points for each question, ***42 points)
1. If (3x+1) 5 = A5X5+A4X4+A3X3+AX2+A1X+A0, then the values of A5-A4+A3-A2+A 1-A0 and A4+A2+A0.
2. If the equation AX-6 = 8 has infinite solutions, what value should A take?
3. If x =-8 is the solution of equation 3x+8 =-a, find the value of A2-4a.
4. If the numerator and denominator of the fraction add positive integers A and B respectively, the result is equal to, then what is the minimum value of A+B?
5. Define the operation "※" in the set of rational numbers, and its rule is a ※ b =-b. Try to find the solution of (x ※ 3) ※ 2 = 1.
6. If there is 1, 4, 7, 10, …, what is the nth number? Take three consecutive numbers from this column, and the total is 48. What are these three numbers? (where n is a positive integer)
7. A cylindrical iron drum with an inner diameter (inner diameter) of 10 cm and a height of 25 cm is filled with water with a depth of 20 cm. Now put a cubic iron block with a length of 5 cm into the iron bucket. How many centimeters will the water level in the bucket rise? If an iron block with a bottom diameter of 6 cm and a height of 20 cm is put into an iron drum, will the water in the iron drum overflow? Why?
Second, the application questions (7 points for each question, ***42 points)
8. Village A has two production teams, A and B, with a total output of 654.38+10,000 kilograms in 2002. After scientific farming, the yield of group A and group B increased by 654.38+00% and 654.38+05% respectively in 2003. If the whole village increased by 654.38+02% in 2003 compared with 2002, we will require 2003a.
9.a works are used alone 10 days, B works are used alone 12 days, C works are used alone 15 days; Party A, Party B and Party C worked for two days first, Party A left, and Party C worked alone for three days, and Party B joined in. How many days will it take to complete?
10. Three people, Party A, Party B and Party C, are running in the same place at the speed of 6m, 4m and 8 m per second on a 400m-long circular track, and Party A and Party B are running in opposite directions. C runs in the opposite direction when it meets B. When it meets B, it meets B in the opposite direction, and so on until A, B and C.
1 1. A company has two engineering teams, A and B, and the number of team A is 28 more than that of team B. Now, due to the need of the task, 20 people are transferred from team B to team A, and the number of team A is twice that of team B. How many people are there in each team?
At 12. 12, the hour hand, minute hand and second hand coincide. How long does it take for the second hand to bisect the angle formed by the hour hand and the minute hand?
13. The distance between A and B is 360 kilometers. A car departs from place A to place B and travels for 72km；. Every hour. Twenty-five minutes after the departure of the A train, the B train departs from B to A with a journey of 48 km. Every hour. After the two cars met, they continued to drive at the original speed and direction. So when the distance between the two cars is 100 km, how long has it been since the car A started?
Third, innovative questions (7 points for each question, *** 14 points)
14. The watch is 3 minutes slower than the standard time every hour. If it is aligned with the standard time of 4: 30 am, then the time indicated by the watch that morning is 10: 50. What is the standard time?
15. A group of mowers have to mow two lawns, the big one is twice as big as the small one. In the morning, people cut the big one, and in the afternoon, they divided it into two parts, half left on the big lawn and the other half cut the small one. In the evening, the big one has just been cut, and the small one has just been cut alone for a day. Ask these mowers.
Four, examination questions (2 points)
16.(2006? The owner of the shop sells a commodity at a price not less than 20% of the purchase price, but in order to get more profits, he sets the price 80% higher than the purchase price. If you want to buy this 360 yuan-priced product, the store can only sell it at the highest price ().
A.80 yuan B. 100 yuan C. 120 yuan D. 160 yuan.
Additional questions-interesting questions in the competition (20 points)
There is a six-digit number, 1, multiplied by 3 to get six digits. Find these six figures.
Knowledge point 1: market economy and discount sales
(1) commodity profit = commodity selling price-commodity cost price (2) commodity profit rate = × 100%.
(3) Commodity sales = commodity sales price × commodity sales volume (4) Commodity sales profit = (sales price-cost price) × sales volume.
(5) If it is sold at dozens of percent of the original price, if it is sold at a 20% discount, it will be sold at 80% of the original price.
1. A shop opened, and all the goods were sold at a 20% discount to attract customers. It is known that when 60 yuan buys a pair of leather shoes, the profit rate of the merchants after 20% discount is 40%. What's the price of this kind of leather shoes? What's the preferential price?
2. A store increased the purchase price of a certain clothing by 40%, then marked it and sold it at a 20% discount. As a result, each piece of clothing still earned 15 yuan. What is the purchase price of each piece of clothing?
A shop increased the purchase price of a bicycle by 45%, then marked the price and sold it at a 20% discount. As a result, every bicycle still earned 50 yuan. What is the purchase price of each bicycle? If the purchase price of each bicycle is X yuan, then the equation listed is ()
a . 45%×( 1+80%)x-x = 50 b . 80%×( 1+45%)x-x = 50
C.x-80%×( 1+45%)x = 50d . 80%×( 1-45%)x-x = 50
4. The purchase price of a commodity is 800 yuan, and the price at the time of sale is 1200 yuan. Later, due to the backlog of this product, the store was prepared to sell it at a discount, but if the profit rate was not less than 5%, it would be discounted at most.
A store first increases the original selling price of a color TV by 40%, and then writes "big reward, 20% discount" in the advertisement. After the customer dismantled it, the demolition department will impose a fine of 2700 yuan per set according to 10 times of the illegal income, so as to seek the original price of each color TV.
Knowledge point 2: Scheme selection
6. If the vegetables of a vegetable company are directly sold in the market, the profit per ton is 1 1,000 yuan; If it is sold after rough machining, the profit per ton can reach 4500 yuan; If it is sold after fine processing, the profit per ton will rise to 7500 yuan. A local company buys this vegetable 1400 tons, and its processing capacity is as follows: if the vegetable is finely processed, it can process 6 tons a day, but the two processing methods cannot be carried out at the same time. Due to seasonality and other conditions, the company must sell or process all these vegetables within 15 days. Therefore, the company has formulated three feasible schemes:
Scheme 1: Roughly process all vegetables.
Scheme 2: Vegetables should be coarsened as much as possible and sold directly in the market before processing.
Scheme 3: Sort out some vegetables and roughly process the remaining vegetables in exactly 15 days.
Which scheme do you think is the most profitable? Why?
7. A city's mobile communication company has opened two kinds of communication services: "GSM" users pay 50 yuan monthly basic fee first, and then pay 0.2 yuan phone bill every 1 minute; "Shenzhouxing" doesn't pay the basic monthly fee, but it needs to pay 1 minute for each call to 0.4 yuan (here refers to local calls). If the call time is x minutes within one month, the charges of the two call modes are 65,438+0 yuan and y2 respectively.
(1) Write the functional relationship between y 1, y2 and x (i.e. equation).
(2) How many minutes do you talk a month, and the cost of the two ways of talking is the same?
(3) If someone expects to use the phone bill of 120 yuan within one month, which call method should he choose?
8. The basic price of domestic electricity for residents in a certain area is 0.40 yuan per kWh. If the monthly electricity consumption exceeds one kWh, the excess will be charged at 70% of the basic electricity price. (1) a household used 84 kwh of electricity in August, and * * * paid 30.72 yuan for electricity, so it was a.
(2) If the average electricity bill of users in September is 0.36 yuan, how many kWh will be used in September? How much should I pay for the electricity?
9. An appliance store plans to buy 50 TV sets from manufacturers for 90,000 yuan. It is known that this manufacturer produces three different models of TV sets, with ex-factory prices of A 1.500 yuan, B 2 1.000 Yuan and C 2500 Yuan respectively.
(1) If the appliance store buys 50 sets of two different models of TV sets at the same time, which costs 90,000 yuan, please study the purchase scheme of the store.
(2) If a shopping mall sells a model A TV set with a profit of 150 yuan, a model B TV set with a profit of 200 yuan and a model C TV set with a profit of 250 yuan, and buys two different TV sets at the same time, which scheme is the most profitable?
10. Xiaogang bought a lamp for the study. There are two kinds of lamps to choose from, one is 9-watt energy-saving lamp, the other is 40-watt incandescent lamp, 18 yuan/lamp. Assuming that the lighting effect of the two lamps is the same, the service life can reach 2800 hours. It is understood that the electricity price of Xiaogang's home is 0.5 yuan per kWh.
(1). If the lighting time is x hours, please use the algebraic expression containing x to indicate the cost of using energy-saving lamps and incandescent lamps respectively. (Cost = price of lamps+electricity fee)
Xiao Gang wants to buy two such lamps. Suppose the lighting time is 3000 hours and the service life is 2800 hours. Please design a lighting scheme with the lowest cost and explain the reasons.
Knowledge point 3 savings and savings interest
(1) The money deposited by the customer in the bank is called the principal, and the reward paid by the bank to the customer is called interest. Principal and interest are collectively referred to as the sum of principal and interest, the time of deposit in the bank is called the number of periods, and the ratio of interest to principal is called the interest rate. Interest tax is paid at 20% of interest.
(2) Interest = principal × interest rate × sum of principal and interest in each period = principal+interest tax = interest × tax rate (20%)
(3)
1 1. A classmate deposited 250 yuan in the bank at one time for half a year. After half a year, * * * got the principal and interest and 252.7 yuan. What is the annual interest rate of the bank for half a year? (excluding interest tax)
2.25 a year
2.70 pounds for three years
Six years 2.88
12. In order to prepare for Xiaoming's college tuition of 20,000 yuan six years later, his father has now participated in education savings. There are three ways to save for education:
(1) directly deposited in 6 years;
(2) Deposit for three years first, and after three years, the principal and interest will be automatically transferred to three years;
(3) Deposit for one year, and then automatically transfer the principal and interest to the next year; What kind of education savings do you think will start with less principal?
13. Xiaogang's father spent 4500 yuan the year before last to buy a two-year bond of a company, which will expire this year. After deducting the interest tax, * * * will get the principal and interest of about 4700 yuan. What is the annual interest rate of this bond (accurate to 0.0 1%)?
14. (Haidian District, Beijing) The purchase price of a commodity in Baiyun Shopping Mall is 8 yuan/piece, and the sales price is 10 yuan/piece (the difference between the sales price and the purchase price is the profit obtained by 2 yuan in selling a commodity). Now, in order to expand sales, the sales price of each commodity is reduced by x%, but the profit obtained by selling a commodity is required to be 90% of the profit obtained before the price reduction, then X.
a . 1 b . 1.8 c . 2d . 10
15. He bought a one-year bond with a few yuan, with an annual interest rate of 10%. After the maturity, he took out half of the principal for shopping, and the remaining half and the interest earned all bought this one-year bond (the interest rate remained unchanged). After the maturity, I got the principal and interest and 1320 yuan. Ask uncle Zhang how much it cost to buy this bond.
Knowledge point 4: engineering problems
Workload = working efficiency × working time = workload ÷ working time
Working hours = workload ÷ work efficiency = sum of workload to complete a task = total workload = 1
16. A job is completed by Party A alone 10 days, and Party B alone completes 8 days. How many days does it take for two people to cooperate?
17. It takes 15 days for a project to be completed by Party A alone and 12 days for Party B alone. Now that Party A and Party B have cooperated for three days, Party A has other tasks, and the remaining projects will be completed by Party B alone. How many days does it take Party B to complete all the projects?
18. the reservoir has two water inlet pipes a and b and a drain pipe C. It takes only six hours to open the A tube to fill the reservoir. The cell can be filled by opening tube B for 8 hours and tube C for 9 hours. If tube A and tube B are opened for 2 hours at the same time, how many hours can the pool be filled after opening tube C?
19. A batch of latest industrial dynamic information is input into the management storage network. Party A does it alone for 6 hours, Party B does it alone for 4 hours, Party A does it for 30 minutes first, and then Party A and Party B do it together. How many hours does it take for Party A and Party B to finish this work together?
20. There are 16 workers in a workshop, and each person can process 5 parts A or 4 parts B every day. Of these 16 workers, some process parts A and the rest process parts B. It is known that each part A can make a profit 16 yuan, and each part B can make a profit in 24 yuan. If this workshop is a * * *.
2 1. It takes Party A 10 days, Party B 12 days and Party C 15 days to do a project alone. Three days after Party A and Party C do it first, Party A has something to leave and Party B takes part in the work. How many days will it take to complete?
Knowledge point five: the law of equivalence relation in some application problems
(1) Sum, Difference, Multiplication and Division. These problems can represent both operational relations and equal relations. Pay special attention to the meaning of keywords in the topic, such as equality, sum difference, multiple, score, more, less, fast, slow and so on. , can guide us to list algebraic expressions or equations correctly. Growth amount = original amount × growth rate cash amount = original amount+growth amount
(2) Equal product deformation problem
The formulas for calculating the area, volume and perimeter of common geometric figures vary with shapes, but the volume remains unchanged.
① Formula of cylinder volume V= bottom area × height = s? h= r2h
② cuboid volume v = length× width× height = =abc
22. The grain in one grain depot is three times that in the second. If 20 tons are taken from the first warehouse and put into the second warehouse, the grain in the second warehouse is the first. How much food is there in each warehouse?
23. Pour the water in the cuboid iron box with the length, width and height of 300mm, 300mm and 80mm filled with water into the cylindrical bucket with the inner diameter of 200mm, and find the height of the cylindrical bucket (accurate to 0. 1mm, ≈ 3. 14).
24. The length, width and height of cuboid A are 260mm, 150mm and 325mm respectively, and the bottom area of cuboid B is 130× 130mm2. I also know that the volume of A is 2.5 times that of B. What is the height of B?
Knowledge point 6: Travel problems
Relationship between basic quantities: distance = speed × time = distance/speed/speed = distance/time.
(1) Encounter problem (2) Tracking problem
Fast spacing+slow spacing = original spacing Fast spacing-slow spacing = original spacing
(3) Navigation problem: downstream (wind) speed = still water (wind) speed+current (wind) speed.
Current (wind) speed = still water (wind) speed-current (wind) speed
Grasp the characteristics of constant distance between the two terminals, constant current speed and constant ship speed (static speed).
25. The distance between Station A and bilibili is 480 kilometers. The local train departs from Station A at a speed of 90km per hour, and the express train departs from bilibili at a speed of140km per hour.
(1) The local train starts first 1 hour, and the express train starts again. The two cars are driving in opposite directions. How many hours after the express train leaves, will the two cars meet?
(2) After two cars started at the same time and walked in opposite directions for several hours, the two cars were 600 kilometers apart?
(3) Two cars start at the same time, and the local train runs in the same direction behind the express train. How many hours later, the distance between the express train and the local train is 600 kilometers?
(4) Two cars leave in the same direction at the same time, and the express train is behind the local train. How many hours will the express catch up with the local train?
(5) After the local train 1 hour, the two cars are driving in the same direction, and the express train is behind the local train. How many hours after the express train leaves, will it catch up with the local train?
The key to this problem is to understand the meaning of opposite direction, opposite direction and same direction, and to understand the driving process. So it can be combined with graphic analysis.
26. Party A and Party B start from Party A and Party B, which are 5 kilometers apart, and walk in the same direction on the same road. Party A's speed is 5 kilometers per hour, and Party B's speed is 3 kilometers per hour. Party A brings a dog. When A catches up with B, the dog catches up with B first, then returns to meet A, then returns to catch up with B, and repeats in turn until A catches up with B. It is known that the speed of the dog is 15.
27. A ship went downstream from A to B, and then returned to C by countercurrent between A and B, sailing for 7 hours. It is known that the speed of the ship in still water is 8 km/h, the current speed is 2 km/h, and the distance between A and C is 10 km. Find the distance between a and b. ..
28. A train must cross the first and second iron bridges at a speed of 600 meters per minute. It takes 5 seconds to cross the second iron bridge than the first one, and knowing that the length of the second iron bridge is 50 meters shorter than that of the first one, try to find the length of each iron bridge.
29. It is known that the distance between Party A and Party B is 120km, and the speed of Party B is faster than that of Party A 1km. Two hours later, Party A will depart from Party A, and Party B will meet Party A in 10 hour. What is the speed of Party A and Party B?
30. A group of students went to military training. On the way, the captain has something to inform from the head to the end of the team. The correspondent returns to the end of the queue at the speed of 18 m/min. The known fleet speed is 14 m/min. Q:? If the captain is known to be 320 meters long, how many minutes will the correspondent return? ? If it is known that the correspondent took 25 minutes, how many meters is the captain?
3 1. An airplane flies between two cities with a wind speed of 24 km/h, and it takes 2 hours and 50 minutes to fly with the wind and 3 hours to fly against the wind. What is the flying distance between the two cities?
32. When a ship sails between Pier A and Pier B, it takes 4 hours to sail downstream and 5 hours to sail upstream. The speed of the current is 2 km/h. Find the distance between terminals a and b.
Knowledge point 7: Numbers.
(1) Need to know the representation method of numbers: the hundredth digit of a three-digit number is A, the tenth digit is B, and the first digit is C (where A, B and C are integers, 1≤a≤9, 0≤b≤9, and 0≤c≤9), then this three-digit number is represented as: 65438. Then grasp the relationship between numbers or between new numbers and original numbers, and find the equation of equal relationship series.
(2) Some representations in the number problem: the relationship between two consecutive integers, the larger one is larger than the smaller one1; Even numbers are represented by 2n, and continuous even numbers are represented by 2n+2 or 2n-2; Odd numbers are represented by 2n+ 1 or 2n- 1.
33. For a three-digit number, the sum of the numbers on the three-digit number is 17, the number on the hundredth digit is 7 larger than that on the decimal digit, and the number on the single digit is 3 times that on the decimal digit. Find this three-digit number
34. For two-digit numbers, one-digit number is twice as large as ten-digit number. If the number of ten digits is reversed with the number of one digit, then the two digits obtained are 36 larger than the original two digits, so the original two digits are found.