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2018 AMC 12B Problem 2

Problem 2 of 25EasierAlgebra

Sam drove 9696 miles in 9090 minutes. His average speed during the first 3030 minutes was 6060 mph (miles per hour), and his average speed during the second 3030 minutes was 6565 mph. What was his average speed, in mph, during the last 3030 minutes?

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Solution

In the first 3030 minutes Sam covered 60⋅12=3060\cdot\tfrac12=30 miles, and in the second he covered 65⋅12=32.565\cdot\tfrac12=32.5 miles. The last 3030 minutes covered 96−30−32.5=33.596-30-32.5=33.5 miles, so the speed was 33.512=67 mph. \dfrac{33.5}{\frac{1}{2}}=67\text{ mph}. Thus, the correct answer is D.

More practice

Concepts: distance rate and time

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