February 2007
Problem of the Month

How Fast Must I Go?

At one point on our trip from Fort Collins to Salt Lake City at Thanksgiving, I noted to my wife that we had gone exactly 80 miles in 90 minutes (so that we were averaging less than 60 miles per hour).

At that point, we were on I-80 traveling on cruise control at the maximum legal speed limit of 75 mph.

How long would it take until we averaged exactly 60 mph from the beginning of the trip?

Solution to the Problem:

It would take 40 minutes or 2/3 hour until we would average 60 mph.
At that point, we would have traveled a total of 130 miles (80 miles plus an additional 50 miles) in a total of 2 1/6 hours (1.5 hours plus an additional 2/3 hour).

I solved this as a Rate-Time-Distance problem.
Let x = time traveled at 75 mph until we reach the 60 mph average.
Then set up a table:

Rate	Time	Distance
----	1.5 hr.	80 miles
75 mph	x hr.	75x miles
60 mph	(1.5 + x) hr.	(80 + 75x) miles

Now, since Rate x Time = Distance, set up the equation:
60 (1.5 + x) = 80 + 75x.
This yields 90 + 60x = 80 + 75x
Solving, we obtain x = 2/3 hour (or 40 minutes).

Correctly solved by:

1. James Alarie	University of Michigan -- Flint Flint, Michigan
2. Sagar Patel	Brookstone School Columbus, Georgia
3. David & Judy Dixon	Bennettsville, South Carolina
4. Shaan Arora	Brookstone School Columbus, Georgia
5. ciuba@bellsouth.net	----------
6. Richard K. Johnson	La Jolla, California
7. Tristan Collins	Virginia Tech Blacksburg, Virginia
8. Neal Amos	Brookstone School Columbus, Georgia
9. John Funk	Ventura, California
10. Mr. Robb's Discrete Math Class	John Handley High School Winchester, Virginia

Send any comments or questions to: David Pleacher