Answer to May 3, 1999 Problem

Going to Work Problem

Michael drove to work at 40 mph and arrived 1 minute late.
The next day, he left at the same time and drove the same distance to work at 45 mph and arrived 1 minute early.

How far did Michael have to drive to work?

Solution to Problem:

The answer is 12 miles.

Let T = number of hours to get to work on time.
Set up a rate-time-distance table as shown below:

Rate Time Distance
40 T + 1/60 40 (T + 1/60)
45 T - 1/60 45 (T - 1/60)

Then set 40 (T + 1/60) = 45 (T - 1/60)

40T + 2/3 = 45T - 3/4

so T = 17/60 hours or 20 minutes.

Hence, the distance = 40 (17/60 + 1/60) = 12 miles.


Correctly solved by:

1. Jia Ran Rome, Italy
2. Jon Pence Winchester, VA
3. Steve Muller Clearbrook, VA
4. Liz Cotter Centreville, VA
5. Bob Hearn Winchester, VA