Question

reasoning tell whether the rates are equivalent.
$7\frac{1}{2}$ miles for every $\frac{3}{4}$ hour
$\frac{1}{2}$ mile for every 3 minutes
\bigcirc$ yes
\bigcirc$ no

Explanation:

Step1: Convert to same time unit

First, convert $\frac{3}{4}$ hour to minutes: $\frac{3}{4} \times 60 = 45$ minutes. Convert $7\frac{1}{2}$ to an improper fraction: $7\frac{1}{2} = \frac{15}{2}$ miles.

Step2: Find rate 1 (miles per min)

Calculate rate for first set: $\frac{\frac{15}{2}}{45} = \frac{15}{2} \times \frac{1}{45} = \frac{1}{6}$ miles per minute.

Step3: Find rate 2 (miles per min)

Calculate rate for second set: $\frac{\frac{1}{2}}{3} = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$ miles per minute.

Step4: Compare the two rates

Both rates equal $\frac{1}{6}$ miles per minute.

Answer:

yes