Question

Isabella and Penelope are both draining their backyard swimming pools. Isabella’s pool holds 1,700 gallons and she is draining the water at a rate of 2.4 gallons per minute. Penelope’s pool holds 1,350 gallons and she is draining the water at a rate of 1.6 gallons per minute. How long will it take to have the same amount of water in both pools?

Answer 1

437 minutes and 30 seconds

Explanation:

That amount of water in both pools can be modeled by a first order equation.

In both cases, the amount of water in the pools will be the initial value decreased at each minute by it's draining rate.

So, for Isabella, the initial amount of water is 1,700 gallons and she is draining at a rate of 2.4 gallons per minute. I will call this equation Wi.

Wi(n) = 1,700 - 2.4n, with n in minutes

For Penelope, the initial amount of water is 1,350 gallons and she is draining at a rate of 1.6 gallons per minute. I will call this equations Wp. So,

Wp(n) = 1,350 - 1.6n

Now we want to know how long it will take for both pools having the same amount of water. This will happen at the value of n for which Wp = Wi, so we solve this equation:

Wi(n) = Wp(n)

1,700 - 2.4n = 1,350 - 1.6n

2.4n - 1.6n = 1,700 - 1,350

0.8n = 350

n = 437.5

So both pools will have the same amount of water in 437 minutes and 30 seconds.