Question

Pool A contains 3500 gallons of water and is increasing at a rate of 50 gallons per minute. Pool B contains 10000 gallons of water and is decreasing at a rate of 80 gallons per minute. In how many minutes will the pools have the same amount of water?

Answer 1

By setting up an equation and solving for time, we determine that Pool A and Pool B will have the same amount of water after 50 minutes.

Step-by-step explanation:

To find out when Pool A and Pool B will have the same amount of water, we can set up an equation to represent the volumes of water in each pool over time. Let's define t as the time in minutes after which the pools will have the same volume.

Pool A's volume increases by 50 gallons per minute, so after t minutes, it will have an additional 50t gallons. Pool B's volume decreases by 80 gallons per minute, so after t minutes, it will have 80t gallons less.

The initial volume of Pool A is 3500 gallons and Pool B is 10000 gallons. The equation that represents the point at which the pools will have the same volume is:

3500 + 50t = 10000 - 80t

Solving for t gives:

50t + 80t = 10000 - 3500

130t = 6500

t = 6500 / 130

t = 50

Thus, after 50 minutes, both pools will have the same amount of water.