AMC 10 2008a Problem 6

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? $\mathrm{(A)}\ 3 \mathrm{(B)}\ 4 \mathrm{(C)}\ 5 \mathrm{(D)}\ 6 \mathrm{(E)}\ 7$