Question

A pool can be filled by a pipe in 3 hours. it takes 3 times as long for another pipe to empty the pool. how long will it take to fill the pool if both pipes are open?

Answer 1

With both the filling and emptying pipes open, it would take 4.5 hours to fill the pool. The key is to find the combined rate by subtracting the emptying rate from the filling rate, then use the combined rate to calculate the total filling time.

Step-by-step explanation:

To solve this problem, one must understand the concept of rates and how they combine when dealing with multiple pipes or sources filling or emptying a pool. A pipe that fills the pool in 3 hours has a filling rate of 1/3 pool per hour. If another pipe takes three times as long to empty the pool, that means it takes 9 hours to empty it, so its emptying rate is 1/9 pool per hour. When both pipes are working together, their rates combine algebraically.

The combined rate of filling and emptying the pool is (1/3 pool/hour - 1/9 pool/hour) = 2/9 pool/hour. To find the total time it would take to fill the pool with both pipes open, divide the total pool volume (1 pool) by the combined rate (2/9 pool/hour).

So, the time to fill the pool with both pipes open is 1 pool / (2/9 pool/hour) = 9/2 hours = 4.5 hours.

Answer 2

There is need 4.5 hours to fill the pool in case if both pipes are open