Question

(7.1a; 7.1b; 7.10)

1. three pipes in a school building are leaking. after 30 minutes, pipe a has leaked $\frac{3}{4}$ gallon of water. after 45 minutes, pipe b has leaked $1\frac{1}{4}$ gallons of water. after 20 minutes, pipe c has leaked $\frac{1}{2}$ gallon of water. which sentence is true?

a pipe a is leaking at the fastest rate.
b pipe c is leaking at the slowest rate.
c pipes a and c are leaking at the same rate.
d pipes a and b are leaking at a faster rate than pipe c.

Explanation:

Step1: Calculate Pipe A's leak rate

Rate = $\frac{\text{Volume}}{\text{Time}} = \frac{\frac{3}{4}}{30} = \frac{3}{4} \times \frac{1}{30} = \frac{1}{40}$ gallons per minute

Step2: Calculate Pipe B's leak rate

Rate = $\frac{\text{Volume}}{\text{Time}} = \frac{1\frac{1}{4}}{45} = \frac{\frac{5}{4}}{45} = \frac{5}{4} \times \frac{1}{45} = \frac{1}{36}$ gallons per minute

Step3: Calculate Pipe C's leak rate

Rate = $\frac{\text{Volume}}{\text{Time}} = \frac{\frac{1}{2}}{20} = \frac{1}{2} \times \frac{1}{20} = \frac{1}{40}$ gallons per minute

Step4: Compare all rates

Pipe A: $\frac{1}{40}$, Pipe B: $\frac{1}{36}$, Pipe C: $\frac{1}{40}$. $\frac{1}{36} > \frac{1}{40}$, so Pipe B is fastest, A and C are equal, and they are the slowest.

Answer:

C. Pipes A and C are leaking at the same rate.