2021 Fall AMC 10A Problem 4

Problem 4 of 25EasierAlgebra

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?

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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 - 0.5}{40} + \dfrac{0.5}{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.