Question

Mr. Lopez has a choice of two routes to get to work. Route A is $6$ miles long, and his average speed along this route is $30$ miles per hour. Route B is $5$ miles long, and his average speed along this route is $40$ miles per hour, except for a $\dfrac{1}{2}$ -mile stretch in a school zone where his average speed is $20$ miles per hour. By how many minutes is Route B quicker than Route A?

$2 \dfrac{3}{4}$

$3 \dfrac{3}{4}$

$4 \dfrac{1}{2}$

$5 \dfrac{1}{2}$

$6 \dfrac{3}{4}$

Solution:

Mr. Lopez would take $\dfrac{6}{30} \cdot 60 = 12$ minutes to travel on Route A.

On Route B, he would take $\left(\dfrac{5 - .5}{40} + \dfrac{.5}{20}\right) \cdot 60 = 8.25$ minutes.

The difference in times along these routes is $12 - 8.25 = 3.75$ minutes.

Thus, B is the correct answer.

2021 AMC 10A Fall Problem 4

Solution:

Problem 4 in Other Years