15. Patrick drives from $\mathrm{P}$ to $\mathrm{Q}$ at an average speed of $40 \mathrm{mph}$. His drive back from $\mathrm{Q}$ to $\mathrm{P}$ is at an average speed of $45 \mathrm{mph}$ and takes two minutes less.
How far, in miles, is it from $\mathrm{P}$ to $\mathrm{Q}$ ?
A 1.5
B 6
C 9
D 12
E 15
15. D Let the distance, in miles, from $\mathrm{P}$ to $\mathrm{Q}$ be $x$.
Then the time taken to travel from $\mathrm{P}$ to $\mathrm{Q}$ is $\frac{x}{40}$ hours $=\frac{3 x}{2}$ minutes.
Also, the time taken to travel from $\mathrm{Q}$ to $\mathrm{P}$ is $\frac{x}{45}$ hours $=\frac{4 x}{3}$ minutes. Therefore $\frac{3 x}{2}-\frac{4 x}{3}=2$. So $\frac{x}{6}=2$. Hence $x=12$.