Answer to September 18, 2000 Problem

The I-81 Problem

 
A certain calculus teacher travels down Interstate 81 from Winchester to Harrisonburg at a constant rate of 60 mph. He returns over the same distance at a constant rate of 30 mph.

What was the average rate of speed over the entire round trip?

 

Solution to Problem:

Answer is 40 mph

Solution:
The distance from Winchester to Harrisonburg is 60 miles, but any distance will work.
Travelling at 60 mph, it would take 1 hour to travel from Winchester to Harrisonburg.
At 30 mph, it would take 2 hours to cover the 60 miles.
Therefore, it would take 3 hours to go the round trip of 120 miles; so the average rate would be 40 mph!
Perhaps it is easier to see in a table:

  Rate Time Distance
Winc. -> Harris. 60 1 60
Harris. -> Winc. 30 2 60
Roundtrip 40 3 120


Correctly solved by:

1. Kirstine Wynn Winchester, VA
2. Jerry Putt Greencastle, PA
3. Court Pifer James Madison University
4. Bob Hearn Winchester, VA
5. David Powell Winchester, VA
6. Joanna Castiglia Winchester, VA
7. Richard Mocarski Virginia Tech
8. Ryan Throckmorton Winchester, VA
9. Joe Vance Winchester, VA
10. Elizabeth Cotter Oak Hill, VA
11. Erin McGinness Winchester, VA