Question

select the correct choice below and fill in any answer boxes to complete your choice.

a. the quantities are proportional because 75 miles in 5 hours has a value of mph, 82.5 miles in 5.5 hours has a value of mph, and the rate for the larger distance is greater than the rate for the smaller distance. (type integers or decimals.)

b. the quantities are proportional because 75 miles in 5 hours has a value of mph, 82.5 miles in 5.5 hours has a value of mph, and these rates are proportional. (type integers or decimals.)

c. the quantities are proportional because both rates have the same value, mph. (type an integer or a decimal.)

d. the quantities are proportional because 75 miles in 5 hours has a value of mph, 82.5 miles in 5.5 hours has a value of mph, and these rates are whole numbers. (type integers or decimals.)

Explanation:

Step1: Calculate rate for 75 miles in 5 hours

Rate is distance divided by time. So, for 75 miles in 5 hours, the rate is $\frac{75}{5} = 15$ mph.

Step2: Calculate rate for 82.5 miles in 5.5 hours

For 82.5 miles in 5.5 hours, the rate is $\frac{82.5}{5.5} = 15$ mph.

Step3: Analyze the options

Since both rates are equal (15 mph), option C is correct as it states the quantities are proportional because both rates have the same value.

Answer:

C. The quantities are proportional because both rates have the same value, $\boldsymbol{15}$ mph.