Chapter 1, Equations and Inequalities - 1.5 Use Problem Solving Strategies and Models - 1.5 Exercises - Problem Solving - Page 39: 32c

$75$ minutes running and $80 $ minutes cycling.

Let $x$ be the time spent running. Then the time spent cycling is $\frac{155}{60}-x$. Then our equation is: $12x+(\frac{155}{60}-x)30=55\\12x+77.5-30x=55\\18x=22.5\\x=1.25$. Thus she spent $75$ minutes running and $80 $ minutes cycling.