September 18, 2000
Problem of the Month

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 the Problem:

Answer is 40 mph

The distance from Winchester to Harrisonburg is 60 miles, but any distance will work.

Traveling 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, Harrisonburg, VA
4. Bob Hearn	Winchester, VA
5. David Powell	Winchester, VA
6. Joanna Castiglia	Winchester, VA
7. Richard Mocarski	Virginia Tech, Blacksburg, VA
8. Ryan Throckmorton	Winchester, VA
9. Joe Vance	Winchester, VA
10. Elizabeth Cotter	Oak Hill, VA
11. Erin McGinness	Winchester, VA

Send any comments or questions to: David Pleacher