13. Two entrants in a school's sponsored run adopt different tactics. Angus walks for half the time and runs for the other half, whilst Bruce walks for half the distance and runs for the other half. Both competitors walk at $3 \mathrm{mph}$ and run at $6 \mathrm{mph}$. Angus takes 40 minutes to complete the course.
How many minutes does Bruce take?
A 30
B 35
C 40
D 45
E 50
Solution
D Angus walks for 20 minutes at $3 \mathrm{mph}$ and runs for 20 minutes at $6 \mathrm{mph} .20$ minutes is one-third of an hour. So the number of miles that Angus covers is $3 \times \frac{1}{3}+6 \times \frac{1}{3}=6$.
Bruce covers the same distance. So Bruce walks $\frac{1}{2} \times 3$ miles at $3 \mathrm{mph}$ which takes him 30 minutes and runs the same distance at $6 \mathrm{mph}$ which takes him 15 minutes. So altogether it takes Bruce 45 minutes to finish the course.