2018 AMC 10B Problem 2

Problem 2 of 25EasierAlgebra

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?

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Solution

Each leg is half an hour. In the first, Sam drove

60 \cdot \tfrac12 = 30

miles; in the second,

65 \cdot \tfrac12 = 32.5

miles. That’s

62.5

miles so far. That leaves

96 - 62.5 = 33.5

miles for the last half hour, which is a speed of

\frac{33.5}{\tfrac12} = 67

mph. Therefore, the answer is D.