2006 AMC 12B Problem 5

Problem 5 of 25EasierAlgebra

John is walking east at a speed of

3

miles per hour, while Bob is also walking east, but at a speed of

5

miles per hour. If Bob is now

1

mile west of John, how many minutes will it take for Bob to catch up to John?

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Solution

Bob closes the gap at a relative speed of

5 - 3 = 2

miles per hour. To cover the

1

-mile gap takes

\frac{1}{2}

hour, or

30

minutes. Thus, the correct answer is A.

Concepts: relative speed · distance rate and time

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.