The answer is 53 seconds.
The formula is (140+125) ÷ (22-17) = 53 seconds.
It can be understood that "from catching up with the rear of the local train to completely overtaking the local train" means that the point at the rear of the local train catches up with the point at the front of the local train, so the catching distance should be the sum of the two captains.
On the 300-meter-long circular runway, both parties set off side by side in the same direction at the same time. The average speed of Party A is 5 meters per second, and that of Party B is 4.4 meters per second. How many meters before the starting line did they meet for the first time?
The answer is 100m.
300 ÷ (5-4.4) = 500 seconds, indicating the catch-up time.
5× 500 = 2500m, indicating the distance traveled when A catches up with B..
2500 ÷ 300 = 8 laps ... 100 meters, which means that the total distance of a chase is 8 laps, which is more than 100 meters, which means that we met before the original starting line 100 meters.
6. Alone by the railway. After hearing the whistle of the distant train, the train passed in front of her 57 seconds later. It is known that the train whistle is at a distance of 1360 meters (the track is straight), and the sound travels 340 meters per second. Find the speed of the train (get the reserved integer).
The answer is 22 meters per second.
Formula:1360 ÷ (1360 ÷ 340+57) ≈ 22m/s.
Key understanding: the car arrives 57 seconds after hearing the sound, which means that the car has already traveled from the place where the sound was made when people heard the sound 1360 ÷ 340 = 4 seconds. That is, it took 4+57 = 6 1.360m * * 0 seconds.
7. The hound found a running hare in front of it at 10 meters away and immediately chased it. The hound took a big step. It ran five steps, and the rabbit ran nine steps, but the rabbit ran very fast. The hound runs two steps, but the rabbit can run three. Ask the hound how many meters it must run to catch up with the rabbit.
The correct answer is that the hound must run at least 60 meters to catch up.
Solution:
From "the hound runs five steps and the rabbit runs nine steps", we can know that for every meter the hound walks, the rabbit walks 5/9 meters. According to "the hound can run 2 steps and the rabbit can run 3 steps", at the same time, the hound can run 2 meters and the rabbit can run 5/9 a * 3 = 5/3 a meters. From this, we can know that the speed ratio between the hound and the rabbit is 2A: 5/3A = 6: 5, that is to say, the hound runs 60 meters and the rabbit runs 50 meters, and the original difference of 10 meter is just used up.
8. In AB, the ratio of time for two people to complete a cycle by bike is 4:5. If two people start exercising from AB at the same time, they will meet after 40 minutes and then move on. How many minutes will B arrive at A later than A arrive at B?
Answer: 18 minutes
Solution: let the whole journey be 1, the speed of a be x, and the speed of b be y.
Column 40x+40y= 1
x:y=5:4
X= 1/72 y= 1/90。
A takes 72 minutes and B takes 90 minutes.
So get the solution.
9. Car A and car B leave relatively from AB at the same time. After the first encounter, the two cars continued to drive and returned immediately after reaching the starting point of the other side. The distance from B to the second meeting is 1/5 of AB's whole journey. It is known that car A traveled 120km when they first met. How many kilometers is AB?
The answer is 300 kilometers.
Solution: Draw a line diagram, and you can know that when two people meet for the first time, they walked 1ab, and from the beginning to the second meeting, they walked 3 AB, so it can be calculated that the distance between A and B is three times that before the first meeting. That is, the distance A * * * walks is 120 * 3 = 360 kilometers. As can be seen from the line chart, A * * * has gone all the way (1+ 1/5).
So 360 ÷ (1+1/5) = 300 km.
It takes 4 hours and 6 hours for two people to ride bicycles from A to B respectively. Now Party A and Party B start from AB and go in opposite directions at the same time. When they meet, they are 2 kilometers away from the midpoint of AB. If two people go to B separately, they will turn back immediately after A ... There is () kilometers between the second meeting point and the first meeting point.
10. It takes 6 hours for a ship to go back and forth at the same speed and go downstream; Countercurrent for 8 hours. If the current speed is 2 kilometers per hour, what is the distance between the two places?
Solution: (1/6-1/8) ÷ 2 =1/48 indicates the fraction of water velocity.
2 ÷ 1/48 = 96 km indicates the total distance.
165438+
Solution:
Meeting is four-seventh of the whole journey, which means that the speed ratio between Party A and Party B is 4: 3.
The time ratio is 3: 4.
So the whole time of the express train is 8/4 * 3 = 6 hours.
6 * 33 =198km
12. Xiaohua travels from A to B, 1 rides, 2/3 rides; Returning from B to A, three-fifths of people rode bicycles and two-fifths rode cars, resulting in a delay of half an hour. It is known that the cycling speed is12km, and the cycling speed is 30km. Q: How many kilometers is it between A and B?
Solution:
Take the distance as 1 and get the time coefficient.
Departure time coefficient: 1/3÷ 12+2/3÷30.
Return time coefficient: 3/5÷ 12+2/5÷30.
The difference between them: (3/5 ÷12+2/5 ÷ 30)-(1/3 ÷12+2/3 ÷ 30) =1/75.
Time to go:1/2× (1/3 ÷12) ÷1/75 and1/2× (2/3 ÷ 30)/kloc-.
Distance:12× [1/2× (1/3 ÷12) ÷1/75]+30× [1/2×
Eight. balanced
1. Party A and Party B are fishing by the river. Party A caught three, and Party B caught two, and was about to eat. One person asked to eat with them, so three people shared the five fish equally. Passers-by left 10 yuan to show their gratitude. How do Party A and Party B share it? quickly
Answer: A accepts 8 yuan and B accepts 2 yuan.
Solution:
"Three people share five fish equally, and the guests take out 10 yuan", which can be understood as the total value of five fish is 30 yuan, so each fish is worth 6 yuan.
Because "A caught three" means that A voted 3 * 6 = 18 yuan before eating, and "B caught two" means that B voted 2 * 6 = 12 yuan before eating.
And the value of both parties is 10 yuan, so
A can also get back 18- 10 = 8 yuan.
B You can also get back 12- 10 = 2 yuan.
It happened to be the money paid by the guests.
2. The cost of a commodity this year has increased by 1 compared with last year, but it still maintains the original selling price, so the profit per share has decreased by two fifths. So, what is the cost of this commodity this year?
Answer 22/25
Thinking about the best line drawing;
If last year's original cost is regarded as 20 shares and profit as 5 shares, then this year's cost will increase by110, that is, 22 shares, while the profit will decrease by 2/5, and this year's profit will be only 3 shares. The increased cost of two copies is exactly the reduced profit of two copies. The price is 25 copies.
So this year's cost accounts for 22/25 of the selling price.
3. Two cars, A and B, start from A and B respectively and go in opposite directions. When they set off, the speed ratio of A to B was 5:4. After they met, A's speed dropped by 20% and B's speed increased by 20%. In this way, when A arrives at B, B is still 10 km away from A, so how many kilometers are A and B apart?
Solution:
It turns out that the speed ratio of A and B is 5:4.
Current A: 5× (1-20%) = 4.
Current B: 4× (1+20%) 4.8.
After A arrives at B, B leaves A: 5-4.8 = 0.2.
Total distance: 10 ÷ 0.2× (4+5) = 450km.
4. The circumference of the cylinder bottom is reduced by 25%, and the volume is increased by 1/3. What is the ratio of the present height to the original height?
The answer is 64: 27.
Solution: According to "the perimeter is reduced by 25%", we know that the perimeter is 3/4, then the radius is 3/4 and the area is 9/ 16.
According to "volume increase 1/3", we can know that the volume is 4/3 of the original.
Volume base area = height
The current height is 4/3 ÷ 9/ 16 = 64/27, which means that the current height is 64/27 of the original height.
Or current height: original height = 64/27: 1 = 64: 27.
Four kinds of fruits, bananas, apples, oranges and pears, were shipped from a market, including 30 tons of bananas and 45 tons of oranges and pears. Oranges account for exactly two-thirds of the total 13. How many tons of fruit did a * * * transport?
Question 2: The answer is 65 tons.
Oranges+apples = 30 tons
Banana+orange+pear = 45 tons
So orange+apple+banana+orange+pear = 75 tons.
Orange (banana+apple+orange+pear) = 2/ 13
Description: 2 oranges, banana+apple+orange arrangement and combination.
If 67 tons of goods are moved from warehouse A to warehouse B, then the goods in warehouse A are exactly twice as much as those in warehouse B; If 17 tons of goods are moved from warehouse A to warehouse B, then the goods in warehouse A are exactly five times that in warehouse B, so how many tons of goods are stored in each warehouse?
67×(2+ 1)- 17×(5+ 1)
=20 1- 102
=99 (ton)
99÷〔(5+ 1)-(2+ 1)〕
=99÷3
=33 (tons) A: It turns out that B has 33 tons.
(33+67)×2+67
=200+67
=267 (tons) A: It turns out that A has 267 tons.
Analysis:
1. If 67 tons of goods are moved from warehouse A to warehouse B, the goods in warehouse A are exactly twice as much as those in warehouse B;
The total number of a and b has not changed. The total includes 2+ 1=3. The current B is the original B plus 67. So the total includes three original B's and three 67 [67× (2+ 1) = 20 1].
2. If 17 tons of goods are moved from warehouse A to warehouse B, then the goods in warehouse A are exactly five times that of warehouse B,
Similarly, the total includes 5+ 1=6 original b and 6 17 (i.e.17× (5+1) =102).
3. It can be seen from 1 and 2 that the difference between the original three B's and the original six B's is only three B's, and the difference between these three B's is exactly 20 1- 102=99 tons. What was the original B? 99÷3=33 tons.
4. seek the original a again.
A travels 12km per hour, and B travels 8km per hour. One day, A went from the east village to the west village, and B went from the west village to the east village at the same time. Thus, when B arrived in the east village, A had already arrived in the west village for five hours. Find out the distance between the two villages.
The distance between Party A and Party B is the same, and the time for Party A is 5 hours less, so it takes t hours to form Party A..
free
1. 12t=8(t+5)
t= 10
So the distance = 120km 1. In order to save energy, a unit collects electricity charges according to the following regulations every month: the electricity consumption does not exceed 140 kwh, and it is charged at 0.43 yuan per kwh; If it exceeds 140 degrees, the excess will be charged at 0.57 yuan per degree. If the average electricity bill charged by Mexican consumers in April is 0.5 yuan per kWh, how much should consumers pay in April?
Let the total power consumption be x degrees: [(x-140) * 0.57+140 * 0.43]/x = 0.5.
0.57 times -79.8+60.2 = 0.5 times
0.07x= 19.6
x=280
Step by step: 140*0.43=60.2
(280- 140)*0.57=79.8
79.8+60.2= 140
2. The ratio of delivery staff to sales staff in the home appliance department of a shopping mall is 1: 8. Due to the obvious increase in the purchase of home appliances this summer, the manager of the home appliance department transferred 22 people from the sales staff to deliver the goods. Results The ratio of delivery staff to sales staff was 2: 5. How many delivery staff and sales staff are there in the home appliance department of this shopping mall?
Suppose there are x delivery people and 8X sales people.
(X+22)/(8X-22)=2/5
5*(X+22)=2*(8X-22)
5X+ 1 10 = 16X-44
1 1X= 154
X= 14
8X=8* 14= 1 12
The home appliance department of this shopping mall used to have 14 delivery staff and 1 12 sales staff.
3. Now a commodity is reduced in price 10% for promotion. In order to keep the sales amount unchanged, how many percent will the sales volume increase over the original price?
Assumption: increase by x%
90%*( 1+x%)= 1
Solution: x = 1/9
Therefore, the sales volume increased by11.11%compared with the original price.
4. The sum of the original unit prices of commodities A and B is 100 yuan. Due to market changes, a commodity decreased by 65,438+00%. B After the price adjustment of commodities rose by 5%, the sum of the unit prices of the two commodities rose by 2%. What are the original unit prices of A and B respectively?
If the original unit price of commodity A is X yuan, then B is100-X.
( 1- 10%)X+( 1+5%)( 100-X)= 100( 1+2%)
The result x = one in X=20 yuan.
100-20=80 B
5. The number of people in Workshop A is 30 less than 4/5 of Workshop B. If 10 people are transferred from Workshop B to Workshop A, then the number of people in Workshop A is 3/4 of Workshop B. Find the original number of people in each workshop.
There are x people in workshop B. According to the equality of the total number, the equation is listed as follows:
X+4/5X-30 = X- 10+3/4(X- 10)
X=250
So the number of people in Workshop A is 250*4/5-30= 170.
Description:
The left side of the equation is adjusted first, and the right side of the equation is adjusted later.
6.A rides a bike from place A to place B, and B rides a bike from place B to place A, both of which move at a constant speed, so that they can start at eight o'clock in the morning at the same time. By morning 10, they were still 36 kilometers apart, and by noon 12, they were 36 kilometers apart. How can we find the distance between a and b? (Equation)
Let the distance between a and b be x.
x-(x/4)=x-72
x=288
Answer: The distance between A and B is 288.
7. The length of car A and car B is 180m. If two trains travel relatively, it takes * * *12s from the time when the front meets the rear; If driving in the same direction, it takes 60 seconds from the front of car A to the rear of car B, and the speed remains unchanged. Find the speed of a car and b car.
The sum of the speeds of the two vehicles is [180 * 2]/12 = 30m/s.
Let the speed of a be x, then the speed of b is 30-X.
180*2=60[X-(30-X)]
X= 18
That is, the speed of car A is 18m/s and the speed of car B is12m/s..
8. Two candles of the same length, the thick one can burn for 3 hours and the thin one can burn for 8/3 hours. When the power goes out, two candles are lit at the same time, and when the phone calls in, they are blown out at the same time. Thick is twice as long as thin. Find out when the power went out.
Suppose the blackout time is X.
Let the total length be 1, then the coarse firing is 1/3 and the fine firing is 3/8.
1-X/3=2[ 1-3X/8]
X=2. Four
Is the power failure 2. Four hours.
9. A factory produced 2300 machines this year, which was 25% higher in the first half of the year and 25% lower in the second half 15%. How many machines were produced in the second half of this year?
Solution: If X production units are set in the second half of the year, [2300-X] units will be produced in the first half of the year.
According to the meaning of the question:1-15% x+1+25% 2300-x = 2300.
Solution: 93 1
A: 93 1 set will be produced in the second half of the year.
10. A rides a bicycle from place A to place B, and B rides a bicycle from place B to place A, both of them are moving at a high speed. You should know that they set off at 8 am at the same time, and by 10 in the morning, they are still 36 kilometers apart, and by noon 12, they are 36 kilometers apart. What's the distance between a and b? ]
Let the distance between a and b be x.
x-(x/4)=x-72
x=288
A: The distance between A and B is 288 meters.
1 1. The fast horse walks 240 miles every day, and the slow horse walks 150 miles every day. Slow horse goes first 12 days. How many days can a fast horse catch up with a slow horse?
The slow horse left 150 days, the fast horse left for 240 days, and the slow horse left first 12 days, that is to say, the distance between the slow horse and the fast horse was150×12 =1800 Li before departure, and then the fast horse set off. This is the fast horse's catch-up speed in a day. The difference between the fast horse and the slow horse is 1800 Li, and the fast horse catches up with 90 Li a day, so 1800÷90=20 days is the number of days when the slow horse catches up with the fast horse.
12. It is known that five A-type machines are full of 8 boxes of products a day, and four B-type machines are full of 1 1 box of products a day, leaving 1. Each type A machine produces 1 product more than type B machine every day. How many products are there in each box?
Let's assume that there are x products in each box.
5 Type A machines: 8x+4
7 B model: 1 1x+ 1.
Because (8x+4)/5 = (11x+1)/7+1.
So: x= 12
So each box contains 12 products.
13. Father and son work in the same factory. It takes my father 30 minutes to walk from home to the factory, and my son only 20 minutes to walk this way. The father left five minutes earlier than his son. How many minutes can he catch up with his father?
Let the total length be "1", then the speed of the father is: 1/30, and the speed of the son is: 1/20.
Let the catch-up time be x.
Father left five minutes early: 1/30*5= 1/6.
x[ 1/20- 1/30]= 1/6
X= 10
That is, the time for my son to catch up is: 10 minutes.
14.200 parts need to be processed. First, A worked alone for five hours, and then worked with B for four hours before finishing the task. It is known that A processes 2 more parts per hour than B. How many parts do A and B process per hour?
Solution: Let B process (x-2) pieces per hour, then A processes X pieces per hour.
According to the total workload such as work efficiency and doubling time:
[(X-2)+X]*4+5X=200
[2X-2]*4+5X=200
8X-8+5X=200
13X=200+8
13X=208
X=208/ 13
X = 16...A.
16-2= 14 (pieces) ... b
A: Then A processes 16 pieces per hour, and B processes 14 pieces.
15. The total length of a bridge is 1000 meters. A train crosses the bridge. It takes 1 minute for the train to cross the bridge completely. The whole train stayed on the bridge for 40 seconds. Find the speed and length of the train.
1 min =60 seconds
If the length of the train is x meters, you can get it according to the meaning of the question.
The speed of the train is (1000+x)/60.
Therefore [(1000+x)/60] * 40 =1000-2x.
The solution is x= 125.
( 1000+x)/60 =( 1000+ 125)/60 = 1 125/60 = 18.75
So the train speed is 18.75 meters per second and the length is 125 meters.
16. Each worker in a workshop can produce 12 bolts or 18 nuts. Each bolt shall be equipped with two nuts. There are currently 28 workers. How to allocate the number of workers so that the daily output just matches?
Solution: Assuming that X individuals are designated to produce bolts, then (28-x) individuals produce nuts.
Because each bolt should have two nuts, the number of bolts is twice as much as the number of nuts.
2× 12x= 18(28-x)
X= 12, so 28-x=28- 12= 16.
That is, 12 people should be allocated to produce bolts and 16 people to produce nuts.
17. Put the sugar in several small squares, 1 square contains 1 grain, the second square contains 2 grains, the third square contains 4 grains, and the fourth square contains 8 grains ... and so on, starting from several squares, there are 448 grains in three consecutive squares?
It is known that sugar is equivalent to a geometric series An with a common ratio of 2, an = 2 (n- 1).
It is required to start from several cells and there are 448 * * * in three consecutive cells. Let the number of sugar in this cell be An, and sum the formula according to the equal proportion series.
[an( 1-2 3)]/( 1-2)= 448，an = 64 = 2 (n- 1)，N=7。
So from the seventh grid, there are 448 * * * in three consecutive grids.
18.200 parts need to be processed. First, A worked alone for five hours, and then worked with B for four hours before finishing the task. It is known that A processes 2 more parts per hour than B. How many parts do A and B process per hour?
Solution: Let B process (x-2) pieces per hour, then A processes X pieces per hour.
According to the total workload such as work efficiency and doubling time:
[(X-2)+X]*4+5X=200
[2X-2]*4+5X=200
8X-8+5X=200
13X=200+8
13X=208
X=208/ 13
X = 16...A.
16-2= 14 (pieces) ... b
A: Then A processes 16 pieces per hour, and B processes 14 pieces.
19. There are 30 tourists, of whom 10 knows neither Chinese nor English. Three people know three times as much English as Chinese. How many people know English but don't know Chinese?
If X people know Chinese, then the number of people who speak English is 3X+3.
Those who know English and Chinese must be greater than or equal to 30- 10.
3X+3+X & gt； = 30- 10 (greater than or equal to)
Those who know English must not exceed 30- 10, that is, less than or equal to.
3X+3 & lt； = 30- 10
17/4 <= X & lt= 17/3
X=5 people (X must be an integer)
Then 3X+3= 18 people.
There are 18+5-20=3 people who know both English and Chinese.
20. The store sells two sets of clothes, each set 135 yuan. According to the cost, a profit of 25%, a loss of 25%. Will the two sets make a profit or lose money?
The store sells two sets of clothes, each set 135 yuan. According to the cost, a profit of 25%, a loss of 25%. Will the two sets share profits or losses?
Let the cost of the first set be x.
X*[ 1+25%]= 135
X= 108
Profit: 135- 108=27 yuan.
The cost of setting up the second group is y.
Y[ 1-25%]= 135
Y= 180
Loss: 180- 135=45 yuan.
So, total loss, loss: 45-27= 18 yuan.
2 1. The cylindrical barrel for drinking water has an inner diameter of 25 cm and an inner wall height of 35 cm. There is a glass with an inner diameter of 6 cm and an inner wall height of 10 cm. How many glasses does it take to put a bucket of drinking water in this glass?
A cylindrical barrel for drinking water has an inner diameter of 25 cm and an inner wall height of 35 cm. There is a glass with an inner diameter of 6 cm and an inner wall height of 10 cm. How many glasses does it take to put a bucket of drinking water in this glass?
Assumption: X-ray glasses are needed.
3 * 3 * 3. 14 * 10 * X = 5 * 5 * 3. 14 * 35
X = 5*5*35/3*3* 10
X = 9.7
A: I need 10 glasses.
22. Ask two workers to make billboards. The master worked alone for four days and the apprentice worked alone for six days. Now the apprentice does 1 day first, and then two people cooperate. Upon completion, 450 yuan will be awarded * * *. If the remuneration is calculated according to the amount of work completed by everyone, how should it be distributed?
Let the total workload be X, the master's efficiency be x/4, the apprentice's efficiency be x/6, and the total efficiency be 5x/ 12. If the apprentice does x/6 in one day, then the time they * * * complete together is 5x/6 divided by 5x/ 12 to get 2 days, which means that it takes 3 days in total.
23. In the second quarter, a canteen saved 3,700 kilograms of coal, including 20% more in May and 25% more in June. How many Jin of coal was saved in the canteen in June?
Solution: Let's save X kilograms in April.
x+( 1+20%)x+( 1+20%)x+25% *( 1+20%)x = 3700
x+ 1.2x+ 1.2x+0.25 * 1.2x = 3700
3.7x=3700
x= 1000
June = April *( 1+20%)( 1+25%)
Then it is equal to:
1000 * (1+20%) * (1+25%) = 3700 (kg)
After investigation, it conforms to the meaning of the question.
A: The canteen saved 3,700 kilograms of coal in June.
24. Father and son work in the same factory. It takes the father 30 minutes to walk from home to the factory, the son only 20 minutes, and the father leaves five minutes earlier than the son. How many minutes can he catch up with his father?
Father and son work in the same factory. It takes the father 30 minutes to walk from home to the factory, the son only 20 minutes, and the father leaves five minutes earlier than the son. How many minutes can he catch up with his father?
Let the total length be "1", then the speed of the father is: 1/30, and the speed of the son is: 1/20.
Let the catch-up time be x.
Father left five minutes early: 1/30*5= 1/6.
x[ 1/20- 1/30]= 1/6
X= 10
That is, the time for my son to catch up is: 10 minutes.