Question

In a race, a bicyclist travels 3 miles in 1/4 hour. Determine the unit rate for the speed

in miles per hour.
3/4 miles per hour
16 miles per hour
11/4 miles per hour
12 miles per hour

Answer 1

Explanation:

the standard measure for speed is

miles per hour.

now we got as measurement

3 miles per 1/4 hour.

to give the standard speed or "unit rate" we assume that the bicyclist maintains the same speed for a whole hour.

and the question is : how many miles is he traveling then in that 1 hour ?

to answer this we have to check how often the actually measured unit of time fits into 1 hour.

1/4 hour fits 4 times into 1 hour.

and that factor applies now also to the miles to keep the value of the rate or ratio unchanged :

miles/time × a/a = miles×a/(time×a)

so that (time×a) = 1 hour

and so, he traveled 3×4 = 12 miles per hour.