Math Question: Man on the Hill

This was a question from my geometry class. We are given at least one warm up question a class, and this was one of those warm ups. I decided to share it with you because it seemed easy until I saw the hint. Then I had to think some more.

This is how we went over it in class:

Problem:
A man drives up a hill at an average speed of 30 mph. Once he gets to the top of the hill he turns around and drives right back down. His average speed for the whole trip is 45 mph. What was his average speed going down the hill?

Hint: the answer is NOT 60.

Calculation:

Let's assume the hill was 30 miles long. It took him an hour to get up the hill (30/30). The entire distance of his trip is 60 miles (30•2). His overall average speed is 45 mph.

Distance=d, Time=t, and Speed=s.

  d/t=s

so...

60/t=45

60=45t

t=1 1/3

It took him 1/3 of an hour to get down the hill.

30/(1/3)=s

(30/1)/(1/3)=90

Answer:
His average speed going down the hill was 90 mph.