Middle School

Two buckets filled with a liquid are leaking. The first bucket leaks at a rate of [tex]\frac{5}{6}[/tex] gallon per [tex]\frac{3}{4}[/tex] hour. The second bucket leaks at a rate of [tex]\frac{3}{8}[/tex] gallon per [tex]\frac{1}{3}[/tex] hour. Which container leaks water less rapidly?

Answer :

The first bucket. 5/6 plus 3/4 is 19/12 and 3/8 plus 1/3 equals 17/24 and 19/12 are bigger

By converting the leakage rates of the two buckets to gallons per hour, it is determined that the first bucket, which leaks at 1.11 gallons per hour, leaks less rapidly than the second bucket, which leaks at 1.125 gallons per hour.

Let's start by finding the rate of leakage for the first bucket: 5/6 gallon per 3/4 hour. To find the rate per hour, we divide 5/6 by 3/4:

(5/6) / (3/4) = (5/6) * (4/3) = 20/18 = 10/9 gallons per hour

Now we'll do the same for the second bucket, which is leaking at a rate of 3/8 gallon per 1/3 hour:

(3/8) / (1/3) = (3/8) * (3/1) = 9/8 gallons per hour

Comparing the two rates, we see that 10/9 gallons per hour is approximately 1.11 gallons per hour, and 9/8 gallons per hour is approximately 1.125 gallons per hour. Therefore, the first bucket leaks less rapidly than the second bucket.

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