Question

A pool has 36 cubic yards of water and is draining at a rate of 3 cubic yards per second. A second pool is empty and filling at a rate of 6 cubic yards per second. At how many seconds, x, will the first pool have less water than the second?

Answer 1

The first pool will never have less water than the second pool since the rate at which the first pool is draining is half the rate at which the second pool is filling.

Step-by-step explanation:

To find the time at which the first pool will have less water than the second, we need to compare the rates at which the first pool is draining and the second pool is filling. The first pool is draining at a rate of 3 cubic yards per second, while the second pool is filling at a rate of 6 cubic yards per second.

Therefore, the first pool will have less water than the second pool when the amount of water drained from the first pool is greater than the amount of water filled into the second pool since the starting amount of water in both pools is the same.

Let's assume it takes x seconds for the first pool to have less water than the second pool. The amount of water drained from the first pool in x seconds is 3x cubic yards, and the amount of water filled into the second pool in x seconds is 6x cubic yards. To find x, we need to solve the equation 3x > 6x, which simplifies to x > 0.

Since the rate at which the first pool is draining is half the rate at which the second pool is filling, the first pool will never have less water than the second pool.

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