2008 AMC 10A Problem 6

Problem 6 of 25EasierAlgebra

A triathlete competes in a triathlon in which the swimming, biking, and running segments are all of the same length. The triathlete swims at a rate of

3

kilometers per hour, bikes at a rate of

20

kilometers per hour, and runs at a rate of

10

kilometers per hour. Which of the following is closest to the triathlete’s average speed, in kilometers per hour, for the entire race?

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Solution

Let each segment have length

x.

The total time is

\dfrac{x}{3} + \dfrac{x}{20} + \dfrac{x}{10} = \dfrac{29}{60}x

hours for the distance

3x.

The average speed is

\dfrac{3x}{\frac{29}{60}x} = \dfrac{180}{29} \approx 6.2,

which is closest to

6.

Thus, the correct answer is D.

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