Question

Mr. Earl E. Bird leaves his house for work at exactly 8:00 A.M. every morning. When he averages $40$ miles per hour, he arrives at his workplace three minutes late. When he averages $60$ miles per hour, he arrives three minutes early. At what average speed, in miles per hour, should Mr. Bird drive to arrive at his workplace precisely on time?

$45$

$48$

$50$

$55$

$58$

Answer: B

Concepts:distance rate and time system of equations

Difficulty rating: 1380

Solution:

Let $t$ be the time in hours to arrive on time. Since three minutes is $0.05$ hours, $40(t+0.05) = 60(t-0.05).$

This gives $40t + 2 = 60t - 3,$ so $t = 0.25.$ The distance is $40(0.25+0.05) = 12$ miles, and the required speed is $\dfrac{12}{0.25} = 48$ miles per hour.

Thus, the correct answer is B.

2002 AMC 12A Problem 11

Answer: B

Difficulty rating: 1380

Solution:

Problem 11 in Other Years