Answer (a little troublesome, I hope to look carefully):
More water can be stored in the pool every 4 hours;
1/3- 1/4+ 1/5- 1/6=7/60
1- 1/6=5/6
Because 5/6 is greater than 7/60*7, so 4*7=28 hours, the pool will not be full. After 28 hours, the pool will keep:
1- 1/6-7/60*7= 1/60
Also need:
(1/60)/(1/3) =1/20 = 0.05 hours.
28+0.05=28.05
That is, after 28.05 hours, water began to overflow the pool.
2. If there is no water in the bucket, it only takes 6-2=4 pumps to finish it in 8 minutes, and 16 minutes takes 4-2=2 pumps to finish it. The number of pumps is inversely proportional to the time, which shows that the conclusion is correct, and it also shows that four pumps can pump out 1/8 barrels of water in one minute, and two pumps can pump out. So in the absence of water, the time required for the pump to complete pumping is:
8/(1/4) =16/(1/2) = 32 minutes, that is,1water pump can pump 1/32 barrels of water in 0 minutes. So a pump can pump 4* 1/32= 1/8 barrels of water in 4 minutes.
So if it takes 4 minutes to finish pumping, in the absence of water, the number of pumps needed is:
1/( 1/8)=8
In addition, two pumps are needed to pump out the make-up water, so the total number of pumps ultimately needed is:
8+2= 10
Answer: If pumping is finished in 4 minutes, you need 10 pumps.
3. It takes 8 hours to fill a pool, 65,438+00 hours to open only 1 pipe, and 65,438+05 hours to open only No.3 pipe. At first, only pipelines 65,438+0,2 were opened, and then pipeline 3 was opened, which took 65,438+00 hours before and after.
Suppose: a pool of water is 1. Water inflow per hour: 1 pipe 1/8, 2 pipes110, 3 pipes1/5. The opening hours of 1 and 2 * * * are (10.25-X) hours, and the opening hours are x hours on the 3rd.
( 1/8+ 1/ 10)( 10.25-X)+ 1/ 15X = 1
9/40(4 1/4-X)+ 1/ 15X = 1
19/ 120 x = 209/ 160
X=33/4
=8* 1/4
That is, 8 hours 15 minutes.
Answer: No.3 pipe was on for 8 hours 15 minutes.
4. A pool with a normally open drain pipe at the bottom and a plurality of water inlet pipes with the same thickness at the top. When the four water inlet pipes are opened, it takes 5 hours to fill the pool. It takes 15 hours to fill the pool with two water inlet pipes open. Now it is necessary to fill the pool within 2 hours. So, how many water inlet pipes should be opened at least?
We assume that the water inflow or outflow of each water pipe per hour is X, and the total amount of pool water is S.
It comes from the meaning of the problem.
4*5x- 1*5x=S
2 * 15x- 1 * 15x = S
Then S= 15*x
Let the Y water pipe fill up in two hours (not two hours).
Then y*2*x-2*x=S, s =15 * x.
y=8.5
So it takes at least two hours to fill nine pipes.
5. There is a bucket. It takes 10 minute to fill water from the outside, and 15 minute to pump water from the inside to the outside. Now we know that when pumping water from the inside out, we can pump 1 m3 of water in one minute. Can you tell me how long it will take to fill this bucket by turning on the tap and pumping water from the outside at the same time?
1÷( 1/ 10- 1/ 15)
= 1÷ 1/30
=30
This bucket can be filled in 30 minutes.