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.

8. The engineering team needs to finish it within the specified date. If Team A does it, it can be finished on schedule. If Team B does it, it will be finished three days later than the stipulated date. If Party A and Party B cooperate for two days first, and then Team B does it alone, it can be completed as scheduled. How many days is the specified date?

The answer is six days.

Solution:

From "If Team B does it, it will be completed three days later than the specified date; If Party A and Party B cooperate for two days first, and then Team B does it alone, it can be completed as scheduled. " ：

B working for three days = a working for two days.

That is, the work efficiency ratio of Party A and Party B is 3: 2.

The working time ratio of Party A and Party B is 2: 3.

The time ratio difference is 1 serving.

The actual time difference is 3 days.

So 3 ÷ (3-2) × 2 = 6 days, which is the time of A, that is, the specified date.

Equation method:

[ 1/x+ 1/(x+2)]×2+ 1/(x+2)×(x-2)= 1

The solution is x = 6.

9. For two candles with the same length, it takes 2 hours to light a thick candle and 1 hour to light a thin candle. One night, the power went out, and Xiao Fang lit two candles to read at the same time. A few minutes later, Xiao Fang put out two candles at the same time and found that the length of the thick candle was twice that of the thin candle. Q: How many minutes was the power cut off?

The answer is 40 minutes.

Solution: Suppose there is a power outage for x minutes.

According to the meaning of the problem in the equation

1- 1/ 120 * x =( 1- 1/60 * x)* 2

The solution is x = 40.