2006 AMC 12B Problem 5

Below is the professionally curated solution for Problem 5 of the 2006 AMC 12B, 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.

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Concepts:relative speed distance rate and time

Difficulty rating: 1100

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?

$30$

$50$

$60$

$90$

$120$

Solution:

Bob closes the gap at a relative speed of $5 - 3 = 2$ miles per hour. To cover the $1$ -mile gap takes $\frac{1}{2} \text{ hour} = 30 \text{ minutes}.$

Thus, the correct answer is A.

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