2009 AMC 10A Problem 4

Question

Eric plans to compete in a triathlon. He can average

2

miles per hour in the

\tfrac14

-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?

\dfrac{120}{11}

11

\dfrac{56}{5}

\dfrac{45}{4}

12

Find the time used by the swim and the run, then subtract from

2

hours

Speed equals

15

miles divided by the leftover time

The swim takes

\dfrac{\frac{1}{4}}{2} = \dfrac18

hour and the run takes

\dfrac{3}{6} = \dfrac12

hour. This leaves

2 - \dfrac18 - \dfrac12 = \dfrac{11}{8}

hours for the bicycle ride.

His average speed must be

\dfrac{15}{\frac{11}{8}} = \dfrac{120}{11}

miles per hour.

Thus, the correct answer is A.

Problem 4 in other years