Answer :
Answer:
Pool 1 leaks faster than pool 2.
Step-by-step 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:
[tex]\displaystyle ROC_1=\frac{2/3}{1/4}=\frac{8}{3}\approx 2.67\ gal/h[/tex]
Pool 2:
[tex]\displaystyle ROC_2=\frac{3/4}{1/3}=\frac{9}{4}= 2.25\ gal/h[/tex]
Comparing both ratios, it's clear pool 1 leaks faster than pool 2.
Pool A is found to be leaking faster at approximately 2.67 gallons per hour, compared to Pool B's 2.25 gallons per hour.
To determine which pool is leaking faster, we need to calculate the rate of leakage for both pools in terms of gallons per hour. This unit rate can be found by setting up a ratio of gallons leaked to the time in hours.
For pool A, it leaked 2/3 gallon in 15 minutes. Since there are 60 minutes in an hour:
Minutes to hours for Pool A: 15 minutes * (1 hour / 60 minutes) = 0.25 hours
Leakage rate for Pool A: (2/3 gallons) / 0.25 hours = 8/3 gallons per hour or approximately 2.67 gallons per hour.
For pool B, it leaked 3/4 gallon in 20 minutes:
Minutes to hours for Pool B: 20 minutes * (1 hour / 60 minutes) = 1/3 hours or about 0.333 hours
Leakage rate for Pool B: (3/4 gallons) / (1/3 hours) = 9/4 gallons per hour or 2.25 gallons per hour.
Comparing the two rates, Pool A is leaking at 2.67 gallons per hour and Pool B is leaking at 2.25 gallons per hour. Hence, Pool A is leaking faster than Pool B.
