Need of Speed For Average Speed

A man drives 1 mile to the top of a hill at 15 mph. How fast must he drive 1 mile down the other side to average 30 mph for the 2-mile trip?

Here is calculation of that speed needed!

Impossible Average Speed Challenge

What was average speed challenge?

A man drives 1 mile to the top of a hill at 15 mph. That means he took, 1/15 hours i.e.4 minutes to reach at the top of a hill.

To achieve average speed of 30 mph, the man has to complete 2 miles trip in 1/15 hours i.e. 4 minutes. But he has already taken 4 minutes to reach at the top of a hill, hence he can't achieve average speed of 30 mph over entire trip. 

MATHEMATICAL PROOF:

Let 'x' be the speed needed in the journey down the hill.

Average Speed = Total Distance/Total time

Average Speed = (1 + 1)/(1/15 + 1/x)

30 = 2/(1/15 + 1/x)

(1/15 + 1/x) = 2 / 30 = 1/15

1/x = 0

x = Infinity/Not defined.

To conclude, it's impossible to achieve average speed of 30mph in trip.