Question

An empty swimming pool can be filled to capacity through an inlet pipe in 3 hours, and it can be completely drained by a drain pipe in 6 hours. if both pipes are fully open at the same time, in how many hours will the empty pool be filled to capacity?

Answer 1

The empty swimming pool can be filled to capacity in 6 hours when both the inlet pipe, which fills the pool at a rate of 1/3 pool per hour, and the drain pipe, which drains it at a rate of 1/6 pool per hour, are fully open at the same time.

Step-by-step explanation:

To solve the problem, we first need to establish the rate at which each pipe can fill or drain the pool. The inlet pipe fills the pool at a rate of 1/3 pool per hour since it can fill the pool in 3 hours. The drain pipe empties the pool at a rate of 1/6 pool per hour as it can drain the pool in 6 hours. When both pipes are open, their rates of filling and draining will combine.

• Inlet pipe's rate: +1/3 pool/hour
• Drain pipe's rate: -1/6 pool/hour

Combined rate when both pipes are fully open:

1/3 - 1/6 = 2/6 - 1/6 = 1/6 pool/hour

Now that we have the combined rate, we want to find the time it takes to fill one full pool. To do this, we simply take the reciprocal of the combined rate:

Time to fill the pool = 1 / (1/6) = 6 hours

Hence, it would take 6 hours to fill the pool to capacity with both pipes fully open.