2009 AMC 10A Problem 4

Eric plans to compete in a triathlon. He can average 2 miles per hour in the \frac{1}{4}-mile swim and 6 miles per hour in the 3-mile run. His goal is to finish the triathlon in 2 hours. To accomplish his goal what must his average speed in miles per hour, be for the 15-mile bicycle ride?

\mathrm{(A)}\ \frac{120}{11} \qquad \mathrm{(B)}\ 11 \qquad \mathrm{(C)}\ \frac{56}{5} \qquad \mathrm{(D)}\ \frac{45}{4} \qquad \mathrm{(E)}\ 12

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.