2006 AMC 12B Problem 5

Attempt Problem 5 of the 2006 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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?

30

50

60

90

120

Bob gains ground at the difference of the two speeds

He must close a

1

-mile gap at

5 - 3

miles per hour

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.

Problem 5 in other years