Question

Mai-Lei completed a local race where she was expected to run and then ride her bicycle. She ran for 12 miles and the biked for 36 miles for a total of 5 hours. If Mai-Lei runs 6 miles per hour slower than she bikes, which equation can be used to calculate the rate at which Mai-Lei biked?

Answer 1

Let r = her biking rate (mph). Then her running rate is r − 6. Time = distance / speed, so

12/(r − 6) + 36/r = 5.

(Equivalently 5r^2 − 78r + 216 = 0, which gives r = 12 mph as the valid solution.)