March 2014
Problem of the Month

Travel Problem

A car was 1/2 mile in front of me as we traveled down a straight road.   If it were going 60 mph and I was traveling at 65 mph, how long would it take for me to catch up to it?   And how far would I have traveled?

Solution to the Problem:

The answer is: 6 minutes and 6.5 miles.

Let x = distance traveled by the other car until I catch up to it.
Then x + 1/2 = distance traveled by me.

Since the other car is traveling at 60 mph, the time it will travel is x / 60.
Since I am traveling at 65 mph, the time I will travel is (x + .5) / 65.
Equate both times since we will have traveled the same amount of time when I catch up to the other car.
So,   x / 60 = (x + .5) / 65.
Then, 65x = 60x + 30
and 5x = 30, so x = 6 miles.

The time elapsed is 6 / 60 = 1/10 hour or 6 minutes.
(Or you could have divided 6.5 by 65 to get the same answer).
The distance I would have traveled is x + .5 = 6 + .5 = 6.5 miles.

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Chad Fore	Gate City, Virginia
3. Patricia Young	John Paul II Catholic High, Tallahassee, Florida
4. Heejung Ahn	John Paul II Catholic High, Tallahassee, Florida
5. Ryan Rignanese	John Paul II Catholic High, Tallahassee, Florida
6. Isaac Kampman	Mountain View High School, Mountain View, Wyoming
7. Adam T. Oakley	----------
8. Ryan Woody	Mountain View High School, Mountain View, Wyoming
9. Sara D'Agostino	Mountain View High School, Mountain View, Wyoming
10. Levi Harmon	Mountain View High School, Mountain View, Wyoming
11. Chelsea Anglen	Mountain View High School, Mountain View, Wyoming

Send any comments or questions to: David Pleacher