Question

a swimming pool holds 600,000 liters of water. the pool has two drainage pipes. when the pool is completely full, the first pipe alone can empty it in 150 minutes, and the second pipe alone can empty it in 100 minutes. when both pipes are draining together, how long does it take them to empty the pool?

Explanation:

Step1: Define rates of each pipe

The first pipe empties 600,000 liters in 150 minutes, so its rate is $\frac{600000}{150} = 4000$ liters per minute. The second pipe empties 600,000 liters in 100 minutes, so its rate is $\frac{600000}{100} = 6000$ liters per minute.

Step2: Combined rate of both pipes

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

Step3: Time to empty the pool together

Using the formula $Time = \frac{Total\ Volume}{Combined\ Rate}$, substitute total volume = 600,000 liters and combined rate = 10,000 liters per minute. So $Time = \frac{600000}{10000} = 60$ minutes.

Answer:

60 minutes