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 $\tfrac{1}{2}$ -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?

$2 \tfrac{3}{4}$

$3 \tfrac{3}{4}$

$4 \tfrac{1}{2}$

$5 \tfrac{1}{2}$

$6 \tfrac{3}{4}$

Solution:

Route A takes $\dfrac{6}{30} = \dfrac{1}{5}$ hour $= 12$ minutes.

Route B has $4.5$ miles at $40$ mph and $0.5$ mile at $20$ mph, taking $\dfrac{4.5}{40} + \dfrac{0.5}{20} = 0.1125 + 0.025 = 0.1375$ hour $= 8.25$ minutes.

The difference is $12 - 8.25 = 3.75 = 3\tfrac{3}{4}$ minutes.

Thus, the correct answer is B.

2021 AMC 12A Fall Problem 3

Solution:

Problem 3 in Other Years