Question

One pump can fill a swimming pool in 4 hours. A second pump can fill the pool in 6 hours. If the pool starts empty, what part of the pool will be filled in each situation? The first pump works for 2 hours and the second pump works for 3 hours.

Answer 1

1/2 of the pool is filled, and in the second situation, the entire pool is filled.

Explanation:

Let's start by finding the hourly filling rate of each pump. The first pump can fill the pool in 4 hours, so its hourly rate is 1/4 of the pool. The second pump can fill the pool in 6 hours, so its hourly rate is 1/6 of the pool.

For the first situation, the first pump works for 2 hours, so it fills 2/4 or 1/2 of the pool. The second pump does not work in this situation, so it fills 0 of the pool. Therefore, the total amount of the pool filled is 1/2.

For the second situation, the first pump works for 2 hours and fills 1/2 of the pool. The second pump works for 3 hours and fills 3/6 or 1/2 of the pool. Therefore, the total amount of the pool filled is 1/2 + 1/2 = 1.

So, in the first situation, 1/2 of the pool is filled, and in the second situation, the entire pool is filled.