Problem:
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?
Answer Choices:
A. 3
B. 4
C. 5
D. 6
E. 7
Solution:
Let x be the length of one segment, in kilometers. To complete the race, the triathlete takes
3x+20x+10x=6029x
hours to cover the distance of 3x kilometers. The average speed is therefore
6029x3x≈(D)6 kilometers per hour. −−−∗TheproblemsonthispagearethepropertyoftheMAA′s[AmericanMathematicsCompetitions](https://maa.org/student−programs/amc/)∗