Question

compute the unit rate. choose all that are correct. a $\frac{1}{2}$ mile in each $\frac{1}{4}$ hour is a rate of $\frac{1}{8}$ miles per hour. b $\frac{1}{2}$ mile in each $\frac{1}{8}$ hour is a rate of 4 miles per hour. c $\frac{1}{5}$ mile in each $\frac{1}{10}$ hour is a rate of 2 miles per hour. d $\frac{1}{2}$ mile in each $\frac{1}{6}$ hour is a rate of $\frac{1}{12}$ miles per hour.

Explanation:

To find the unit rate (miles per hour), we use the formula: Unit Rate = Distance / Time. We'll check each option one by one.

Step 1: Check Option A

Distance = $\frac{1}{2}$ mile, Time = $\frac{1}{4}$ hour.
Unit Rate = $\frac{\frac{1}{2}}{\frac{1}{4}}$ = $\frac{1}{2} \times \frac{4}{1}$ = 2 miles per hour. But the option says $\frac{1}{8}$ miles per hour. So, A is incorrect.

Step 2: Check Option B

Distance = $\frac{1}{2}$ mile, Time = $\frac{1}{8}$ hour.
Unit Rate = $\frac{\frac{1}{2}}{\frac{1}{8}}$ = $\frac{1}{2} \times \frac{8}{1}$ = 4 miles per hour. The option says 4 miles per hour. So, B is correct.

Step 3: Check Option C

Distance = $\frac{1}{5}$ mile, Time = $\frac{1}{10}$ hour.
Unit Rate = $\frac{\frac{1}{5}}{\frac{1}{10}}$ = $\frac{1}{5} \times \frac{10}{1}$ = 2 miles per hour. The option says 2 miles per hour. So, C is correct.

Step 4: Check Option D

Distance = $\frac{1}{2}$ mile, Time = $\frac{1}{6}$ hour.
Unit Rate = $\frac{\frac{1}{2}}{\frac{1}{6}}$ = $\frac{1}{2} \times \frac{6}{1}$ = 3 miles per hour. But the option says $\frac{1}{12}$ miles per hour. So, D is incorrect.

Answer:

B. $\frac{1}{2}$ mile in each $\frac{1}{8}$ hour is a rate of 4 miles per hour.
C. $\frac{1}{5}$ mile in each $\frac{1}{10}$ hour is a rate of 2 miles per hour.