1.A and b water pipes need 20 hours and 16 hours to open and fill a pool of water respectively. It takes 10 hour for water pipe c to be opened alone. If there is no water in the pool, open water pipes A and B at the same time. After 5 hours, open the drain pipe C again. How many hours does it take to fill the swimming pool?
Solution:
1/20+116 = 9/80 indicates the working efficiency of both parties.
9/80× 5 = 45/80 indicates the water quantity after 5 hours.
1-45/80 = 35/80 indicates the required water intake.
35/80 ÷ (9/80-110) = 35 means it takes 35 hours to fill it.
A: It will take 35 hours to fill the pool after 5 hours.
2. It takes 20 days for Team A to build a canal, and 30 days for Team B to build it alone. If two teams cooperate, the work efficiency will be reduced because of the influence of each other's construction. The working efficiency of team A is four fifths of the original, while that of team B is only nine tenths of the original. Now it is planned to complete the canal in 16 days, and it is required that the two teams cooperate for as few days as possible. So how many days will the two teams cooperate?
Solution: From the meaning of the question, the work efficiency of Party A is 1/20, that of Party B is 1/30, and that of both parties is1/20 * 4/5+1/30 * 9//kloc-0. A's work efficiency >: B's ergonomics.
Because it is required that "the fewer days the two teams work together, the better", Party A should be made to work faster./kloc-If it is too late within 0/6 days, Party A should cooperate with Party B.. Only in this way can the two teams work together as little as possible.
Let the cooperation time be x days, then Party A will do it alone for (16-x) days.
1/20 *( 16-x)+7/ 100 * x = 1
x= 10
A: The shortest cooperation period between Party A and Party B is 10 day.
It takes 4 hours for Party A and Party B to do a job, and 5 hours for Party B and Party C to do a job. Now, please ask Party A and Party C to work together for 2 hours, and the remaining Party B needs to work for 6 hours. How many hours does it take to finish the work alone?
Solution:
According to the meaning of the question, 1/4 means Party A 1 hour, and Party B +0/5 means Party C 1 hour.
(1/4+1/5) × 2 = 9/10 means that Party A worked for 2 hours, Party B worked for 4 hours and Party C worked for 2 hours.
According to "After Party A and Party C work together for 2 hours, Party B needs to work for 6 hours", we can know that the workload of Party A working for 2 hours, Party B working for 6 hours and Party C working for 2 hours is 1.
So1-9/10 =110 means that B works for 6-4 = 2 hours.
110 ÷ 2 =1/20 indicates the work efficiency of Party B. ..
1 ÷ 1/20 = 20 hours means that it takes 20 hours for Party B to complete it alone.
A:B It takes 20 hours to finish it alone.
4. For a project, Party A will do it on the first day, Party B will do it on the second day, Party A will do it on the third day and Party B will do it on the fourth day, and it will be completed in integer days. If B does it on the first day, A does it on the second day, B does it on the third day and A does it alternately on the fourth day, then the completion time will be half a day longer than last time. It is known that it takes 17 days for B to do this project alone. A How many days does it take to do this project alone?
Solution: According to the meaning of the problem,
1/A+ 1/B+ 1/A+ 1/B+…+ 1/A = 1。
1/B+ 1/A+ 1/B+ 1/A+…+ 1/B+ 1/A×0.5 = 1。
(1/ A represents the working efficiency of A, 1/ B represents the working efficiency of B, and the final outcome must be as shown in the above figure, otherwise the second method will not be 0.5 days longer than the first one).
1/a =1/b+1/a× 0.5 (because the previous workload is equal).
Get 1/ A = 1/B× 2.
Because1/b =117.
So 1/ A = 2/ 17, and A = 17 ÷ 2 = 8.5 days.
Master and apprentice both process the same number of parts. When the master finishes12, the apprentice finishes 120. When the master finished the task, the apprentice finished 4/5 of this batch of parts. How many?
The answer is 300.
120 ÷ (4/5 ÷ 2) = 300
You can think of it this way: 1/2 for the first time and 1/2 for the second time are all done at once. Then after the second time, the apprentice completed 4/5, and it can be inferred that half of the 4/5 completed for the first time is 2/5, which is exactly 120.
6. A batch of saplings, if distributed to boys and girls, will average 6 saplings per person; If you plant a single copy for girls, each person will plant 10 trees on average. One for boys, how many trees per person?
The answer is 15 trees.
Formula:1÷ (1/6-110) =15 trees.
7. A pool is equipped with three water pipes. Tube A is the water inlet pipe, tube B is the water outlet pipe, which can fill the pool water in 20 minutes, and tube C is also the water outlet pipe, which can fill the pool water in 30 minutes. Now, first open the first pipe. When the water in the pool just overflows, it takes 18 minutes to open the second and third pipes. When the first pipe is filled with water, open the second pipe instead of the third one. How many minutes does it take to finish drinking water?
The answer is 45 minutes.
1÷ (1/20+1/30) =12 indicates the number of minutes required for Party B and Party C to jointly drain the full pool water.
112 * (18-12) =112 * 6 =12, that is to say, with the cooperation of Party B and Party C, the overflow pond
1/2 ÷18 =1/36 means that A enters the water once every minute.
Finally,1÷ (1/20-1/36) = 45 minutes.
Lan Xia Lan [Department Head Level 4] Lan Xia Lan [Department Head Level 4] went to TA's house to see the questions that Ta had answered. Tribal charm: 1 3/100 Quick question intelligence: 4 1820/200 1 square vitality: 10 0 0/50 Answer adopted.
The evaluation has been closed, and there are currently 0 comments.
Is that OK
0% (0)0% (0)
relevant issues
Question and answer of fifth grade Olympic mathematics
Fourth grade, the first question and answer of Olympic Mathematics.
Junior high school olympiad math test questions and answers
Urgent need: several junior middle school Olympic math problems and their analysis
Sixth grade (whole book) mathematical resources and evaluation Beijing Normal University Edition answer Sixth grade (whole book) mathematical resources and evaluation Beijing Normal University
There is an urgent need for 30 application questions, which should be difficult. Sixth-grade pupils should have answers, and the answers are behind them. Don't put them together! ! ! Please, everyone.
Look at the same topic: Grade One Chinese Learning Game 6 1 1 Year Mathematics Game: Mathematics Game Grade One Mathematics Comor Manor reporter seeks the answer.
Other answers (***7)
1. There are 28 children waiting in line. The number from the left 10 is Aihua. What's the number on his right?
2. new york time is HK time minus 13 hours. You have an appointment with a friend in new york to call him at 8 pm on April 1 new york time. When should you call him in Hong Kong?
A worker can process 90 parts in 5 hours. /kloc-how many workers does it take to process 540 parts in 0/0 hour?
4. How many integers greater than 100 have the same quotient and remainder after dividing by 13?
5. Four rooms, with no less than two people in each room and no less than eight people in any three rooms. How many people are there in these four rooms?
6. The divisor (or factor) of1998 has two digits, which is the largest?
7. In the English exam, Xiao Ming scored an average of 88 points in the first three times. How many points does he get if he wants to average 90 points for the fourth time?
8. There are at most five Sundays in a month. 12 What are the months with five Sundays in a year?
9. Choose six of the ten numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, and fill in the following boxes to make the formula hold. Each box is filled with a number, and the number in each box is different.
□ +□□ =□□□
What is the largest three digits in the formula?
10. A number is six digits, the first four digits are 2857, and the last two digits are unclear, namely
2857□□
But I remember it can be divisible by 1 1 and 13. Please work out the last two figures.
1 1. A school has 5 18 students. If the number of boys increases by 4% and the number of girls decreases by 3, the total number will increase by 8. So how many more boys than girls?
12. Chen Min wants to go shopping three times. 5 yuan, 2 yuan, 1 yuan, how many coins should I bring * * * so that I don't generate any change below 10 yuan at a time?
(There are only three kinds of coins: 5 yuan, 2 yuan, 1 yuan. )
13. The figure on the right is a graph composed of three semicircles, in which the diameter of the small circle is 8 and the diameter of the middle circle is 12.
14. The kindergarten teacher sent some pictures to Class A, Class B and Class C, and everyone can get 6 pictures. If it is only Grade B, everyone can get 15 pictures. If it is only Grade C, everyone can get 14 pictures. If it is Class A, how many photos can each person get?
15. Two people play a game: take turns to count off, and the count off can only be 1, 2, 3, 4, 5, 6, 7, 8. Add up the figures reported by two people. After the number is reported, the plus sign is 123, and the winner will give priority to the number.
16. The page number of the novel must be printed in the font of 1989. 1 How many times does this number appear in the page number of this book?
What are the last four digits of the sum of 17.23: 3, 33, 333, …, 33…3(23 3s)?
18. Arrange the eight numbers 1, 1, 2, 2, 3, 4, 4 into an eight-digit number, so that there is a number between two 1, two numbers between two 2, three numbers between two 3 and two 4. So, here's the thing.
19. Take at most a few numbers from the natural number 1, 2, 3, …, 2004, 2005, so that the difference between every two numbers is not equal to 4?
20. There is a six-digit telephone number, in which the three digits on the left are the same, and the three digits on the right are three consecutive natural numbers, and the sum of the six digits is exactly equal to the last two digits. What's the phone number?
2 1. If a is a natural number, prove 10 │ (A2005-A 1949).
22. Give 12 different two-digit numbers, and prove that two numbers can be selected from them, and their difference is a two-digit number composed of two identical numbers.
23. Find the smallest three digits of 2 divided by 3, 3 divided by 5 and 5 divided by 7.
24. Let 2n+ 1 be a prime number, and prove that:12,22, …, n2 is divided by 2n+ 1 to get different remainders.
25. The difference between the sum of squares of prime numbers not less than 5 1 will be divisible by 24.
26. There are two kinds of sugar water, A contains 270g of sugar, 30g of water, B contains 400g of sugar, and water100g. Now we want to get100g of 82.5% sugar water. How many grams should we take from everyone?
27. A container contains 65,438+00 liters of pure alcohol. After pouring out 1 l, fill it with water, then pour out 1 l, and then pour out 1 l. What is the concentration of alcohol solution in the container?
28. A few kilograms of 4% salt water evaporated part of the water and became 10% salt water. After adding 300 grams of 4% salt water, it becomes 6.4% salt water. How many kilograms was the original salt water?
29. It is known that a few grams of salt water, after adding a certain amount of water for the first time, the concentration of salt water becomes 3%, and after adding the same amount of water for the second time, salt
Enough! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !