2021 AMC 12A Fall Problem 3

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}

Route A takes

\dfrac{6}{30}

hour; convert to minutes

Route B splits into

4.5

miles at

40

mph and

0.5

mile at

20

mph

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.

Problem 3 in other years