Question

a swimming pool holds 660,000 liters of water. the pool has two drainage pipes. when the pool is completely full, the first pipe alone can empty it in 110 minutes, and the second pipe alone can empty it in 165 minutes. when both pipes are draining together, how long does it take them to empty the pool?

Explanation:

Step1: Find rates of each pipe

The first pipe empties 660,000 liters in 110 minutes, so its rate is $\frac{660000}{110} = 6000$ liters per minute.
The second pipe empties 660,000 liters in 165 minutes, so its rate is $\frac{660000}{165} = 4000$ liters per minute.

Step2: Combined rate

When working together, their combined rate is $6000 + 4000 = 10000$ liters per minute.

Step3: Time to empty together

Using the formula $Time = \frac{Total\ Volume}{Combined\ Rate}$, we substitute the total volume (660,000 liters) and combined rate (10,000 liters per minute):
$Time = \frac{660000}{10000} = 66$ minutes.

Answer:

66 minutes