John is a trail runner who decides to take a day off work to run up

Hi Gnpth,

These types of "weighted average" questions can be solved in a number of different ways. Here's how you can solve it by TESTing VALUES.

We're told that the distance UP the mountain and DOWN the mountain are the SAME, and that John's respective speeds are 5 miles/hour UP and 7 miles/hour DOWN. We're asked for the AVERAGE SPEED for the entire run. Since we're not given a distance, we can test ANY distance we like. By making the one-way distance 35 miles, we can make most of the 'math' easy to deal with.

UP:
Dist = (Rate)(Time)
35mi = (5mph)(T)
35/5 = T
7 hours = T

DOWN:
Dist = (Rate)(Time)
35mi = (7mph)(Time)
35/7 = T
5 hours = T

The formula for AVERAGE SPEED is...

Total Distance = (Average Speed)(Total Time)

The total distance is 35+35 = 70 miles and the average time is 7+5 = 12 hours...

70mi = (Av. Sp)(12 hours)
70/12 = Av. Sp.
35/6 =
5 5/6 miles/hour

Final Answer:

GMAT assassins aren't born, they're made,
Rich