2002 AMC 10A Problem 12

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 linear equation

Difficulty rating: 1410

Small hint:

Let

t

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

0.05

hours

Big hint:

The distance is the same both ways:

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

Solution:

Let

t

hours be the on-time travel time. Since

3

minutes is

0.05

hours,

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

Then

40t+2=60t-3,

so

t=0.25.

The distance is

40(0.30)=12

miles, so the required speed is

\dfrac{12}{0.25}=48

mph.

Thus, the correct answer is B.