Problem:
The AIME Triathlon consists of a half-mile swim, a -mile bicycle ride, and an eight-mile run. Tom swims, bicycles, and runs at constant rates. He runs five times as fast as he swims, and he bicycles twice as fast as he runs. Tom completes the AIME Triathlon in four and a quarter hours. How many minutes does he spend bicycling?
Solution:
Let be the rate that Tom bicycles in minutes per mile. Then Tom runs at the rate of and swims at the rate of . Because four and a quarter hours is minutes,
This simplifies to , so . Tom bicycles at the rate of minutes per mile, so the number of minutes he spends bicycling is .
The problems on this page are the property of the MAA's American Mathematics Competitions