Question

John is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 5 miles per hour and returns along the same route at an average speed of 7 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain?

(A) 5.5
(B) 5.8
(C) 6.0
(D) 6.3
(E) 6.5

Answer 1

(C) 6.0
What you first want to do to find the average speed is add 5 miles and 7 miles together. You don’t need to convert the time because they both are in mph. Then you divide it by 2, getting the average of the trip up and down the mountain. If you need to find the average of something, use the mean formula.

Answer 2

Average speed

= 5 5/6 mph , or

= 5.83 mph (to 2 decimals)

Explanation:

Average speed is total distance divided by the total time it takes to cover the given distance.

Since uphill = 5 mph, and downhill = 7 mph, we know the average speed is between 5 and 7 mph.

Let

x = distance uphill, and also distance downhill.

Total distance = 2x miles

Total time = x/5 + x/7 hours = 12x/35 hours

Average speed

= total distance/total time

= 2x / (12x/35) mph

= 70x / 12x

= 5 5/6 mph

= 5.83 mph (to 2 decimals)