Question

Comparing Leaking Pool Problem

Two pools are leaking. After 15 minutes, pool A has leaked ⅔ gallon. After 20 minutes, pool B has leaked ¾ gallon. Which pool is leaking faster? Hint: The unit rates must be in gallons per hour.

Answer 1

Pool 1 leaks faster than pool 2.

Explanation:

Rates of change

The rate of change (ROC) is a measure that compares two quantities, usually to know how fast one variable changes in time.

We are given two rates of change for two pools that are leaking. The first one loses 2/3 gallon in 15 minutes, and the other loses 3/4 gallon in 20 minutes.

To compare them, we are required to express time in hours. Recall one hour has 60 minutes, or equivalently, one minute has 1/60 hours. Converting both times, we have:

15 minutes = 15/60 = 1/4 hours

20 minutes = 20/60 = 1/3 hours

Now compute both rates of change:

Pool 1:

`\displaystyle ROC_1=(2/3)/(1/4)=(8)/(3)\approx 2.67\ gal/h`

Pool 2:

`\displaystyle ROC_2=(3/4)/(1/3)=(9)/(4)= 2.25\ gal/h`

Comparing both ratios, it's clear pool 1 leaks faster than pool 2.