Question

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?

$3$

$4$

$5$

$6$

$7$

Answer: D

Concepts:distance rate and time harmonic mean

Difficulty rating: 1100

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.

2008 AMC 10A Problem 6

Answer: D

Difficulty rating: 1100

Solution:

Problem 6 in Other Years