Question

В бассейне проведены три трyбы.С помощью первой трyбы бассейн можно наполнить за 10 ч. ,с помощью второй- за 8 ч., с помощью третьей трyбы вся вода из наполненного бассейна может вылиться за 5 ч. Какая часть бассейна бyдет наполнена за 1 ч .,если бyдyт открыты все три трyбы

Answer 1

  за час первая труба наполнит 1/10 части бассейна  
  за час вторая труба наполнит 1/8части бассейна

за час через третью выльется 1/5 части бассейна
1\10+1/8=4/40+5/40=9/40  части наполнится  через 2трубы(
Но через 3 трубу  вода выливается !!!!!!!!!!!!
9\40-1\5=9\40-8\40=1\40 часть бассейна бyдет наполнена за 1 ч .,если бyдyт открыты все три трyбы

Можно  сделать в одно деиствие ....так проще...

1/10+1/8-1/5=4/40+5/40-8/40=1\40

Answer 2

Problem Analysis

We are given three pipes in a pool. The first pipe can fill the pool in 10 hours, the second pipe can fill the pool in 8 hours, and the third pipe can empty the pool in 5 hours. We need to determine what fraction of the pool will be filled in 1 hour if all three pipes are open.

Solution

To solve this problem, we need to find the rates at which each pipe fills or empties the pool. We can then calculate the combined rate at which the pool is being filled or emptied when all three pipes are open.

Let's denote the rates at which the first, second, and third pipes fill or empty the pool as R1, R2, and R3, respectively. We can calculate these rates using the formula:

Rate = Volume / Time

For the first pipe, the rate at which it fills the pool is:

R1 = 1 pool / 10 hours = 1/10 pool per hour

For the second pipe, the rate at which it fills the pool is:

R2 = 1 pool / 8 hours = 1/8 pool per hour

For the third pipe, the rate at which it empties the pool is:

R3 = 1 pool / 5 hours = -1/5 pool per hour (negative sign indicates emptying)

Now, let's calculate the combined rate at which the pool is being filled or emptied when all three pipes are open. We can add the rates of the filling pipes and subtract the rate of the emptying pipe:

Combined Rate = R1 + R2 + R3

Substituting the values of R1, R2, and R3, we get:

Combined Rate = 1/10 + 1/8 - 1/5

To simplify this expression, we need to find a common denominator for the fractions. The least common multiple (LCM) of 10, 8, and 5 is 40. Multiplying each fraction by the appropriate factor to get a denominator of 40, we get:

Combined Rate = 4/40 + 5/40 - 8/40 = 1/40 pool per hour

Therefore, when all three pipes are open, the pool is being filled at a rate of 1/40 of the pool per hour.

Answer

If all three pipes are open, 1/40 of the pool will be filled in 1 hour.

Example Calculation

Let's verify our answer with an example calculation. If the pool has a capacity of 40 liters, and all three pipes are open for 1 hour, the amount of water filled in the pool would be:

Amount filled = Rate * Time = (1/40) * 1 = 1/40 pool

So, in this example, 1/40 of the pool would be filled in 1 hour, which matches our previous answer.

Conclusion

In conclusion, when all three pipes are open, 1/40 of the pool will be filled in 1 hour.