Question

two pools are being filled with water. to start, the first pool contains 795 liters of water and the second pool is empty. water is being added to the first pool at a rate of 17.25 liters per minute. water is being added to the second pool at a rate of 43.75 liters per minute.
after how many minutes will the two pools have the same amount of water?
minutes
how much water will be in each pool when they have the same amount?
liters

Explanation:

Step1: Define variables and set up equation

Let \( t \) be the number of minutes. The amount of water in the first pool after \( t \) minutes is \( 795 + 17.25t \) liters, and the amount in the second pool is \( 43.75t \) liters. We set them equal: \( 795 + 17.25t = 43.75t \)

Step2: Solve for \( t \)

Subtract \( 17.25t \) from both sides: \( 795 = 43.75t - 17.25t \)
Simplify the right side: \( 795 = 26.5t \)
Divide both sides by \( 26.5 \): \( t = \frac{795}{26.5} = 30 \)

Step3: Find the amount of water

Substitute \( t = 30 \) into the second pool's equation (or first, since they are equal): \( 43.75 \times 30 = 1312.5 \) liters

Answer:

After 30 minutes, the two pools will have the same amount of water. Each pool will have 1312.5 liters of water.