High School

Two containers filled with water are leaking.

Container A leaks at a rate of [tex]\frac{2}{3}[/tex] gallon every [tex]\frac{1}{4}[/tex] hour.

Container B leaks at a rate of [tex]\frac{3}{4}[/tex] gallon every [tex]\frac{1}{3}[/tex] hour.

Determine which container is leaking water more rapidly.

Answer :

Final answer:

Container B is leaking water more rapidly than container A.

Explanation:

To determine which container is leaking water more rapidly, we can compare the rates at which each container is leaking. Container A is leaking at a rate of 2/3 gallon every 1/4 hour, which can be simplified to 8/12 gallon every 1/4 hour. Container B is leaking at a rate of 3/4 gallon every 1/3 hour, which can be simplified to 9/12 gallon every 1/3 hour.

To compare these rates, we need to find a common denominator. The least common multiple of 12 and 3 is 12, so we can rewrite the rates as 8/12 gallon every 1/4 hour and 9/12 gallon every 1/3 hour.

Now we can compare the rates directly. Since 8/12 is less than 9/12, container A is leaking water at a slower rate than container B. Therefore, container B is leaking water more rapidly.