2002 AMC 12A Problem 11

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

Small hint:

Let

t

be the on-time travel time in hours; three minutes is

0.05

hours

Big hint:

Set

40(t+0.05) = 60(t-0.05),

solve for

t,

then find the distance

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.