2002 AMC 10A Problem 12

Below is the professionally curated solution for Problem 12 of the 2002 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 10A solutions, or check the answer key.

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Concepts:distance rate and time linear equation

Difficulty rating: 1410

12.

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?

$45$

$48$

$50$

$55$

$58$

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.

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