2018 AMC 12B Problem 2

Below is the professionally curated solution for Problem 2 of the 2018 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2018 AMC 12B solutions, or check the answer key.

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Concepts:distance rate and time

Difficulty rating: 1080

Sam drove $96$ miles in $90$ minutes. His average speed during the first $30$ minutes was $60$ mph (miles per hour), and his average speed during the second $30$ minutes was $65$ mph. What was his average speed, in mph, during the last $30$ minutes?

$64$

$65$

$66$

$67$

$68$

Solution:

In the first $30$ minutes Sam covered $60\cdot\tfrac12=30$ miles, and in the second he covered $65\cdot\tfrac12=32.5$ miles.

The last $30$ minutes covered $96-30-32.5=33.5$ miles, so the speed was $\dfrac{33.5}{1/2}=67\text{ mph}.$

Thus, the correct answer is D.

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