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?


5
(
36
x
)
=
12
x
−
6


12
x
+
36
x
−
6
=
5


36
x
+
12
x
−
6
=
5


36
x
=
12
5
−
x

Answer 1

Let x = her biking speed (mph). Then biking time = 36/x and running time = 12/(x − 6). Total time 5 hours, so

36/x + 12/(x − 6) = 5.

(Also require x > 6.)