CPM Homework Help : PC3 Problem 3-96

Deja wants a coffee from Luckstars, but the store closes very soon. She drives as fast as she can, $45$ mph, to get to the store before they close. On the way back she is relaxed and drives at half the speed. Assuming that she drives on the same straight road with no traffic or stops both there and back, what is her average driving speed?

Hint:

$\text{average speed}=\frac{\text{total distance}}{\text{total time} }$

Step 1:

Let the distance to Luckstars $=x$ . Then Deja's time on the way to Luckstars is $\frac{x}{45}$ .

Step 2:

The distance on the return trip is also $=x$ . Deja's time on the return trip is $\frac{x}{22.5}$ since Deja's rate is $\frac{45}{2}=22.5$ mph.

Step 3:

$\frac{\text{total distance}}{\text{total time}}=\frac{x+x}{\frac{x}{45}+\frac{x}{22.5}}$

Now simplify this complex fraction.