Answer to April 15, 2002 Problem
from Ask Marilyn

the Jogging Problem

 
A woman is jogging across the Handley Railroad bridge. When she is 3/8ths of the way across, she hears a train coming from behind her. She calculates that if she keeps running, she will reach the end of the bridge at the same instant as the train.

She also calculates that if she turns around and runs back, she will reach the beginning of the bridge at the same instant as the train.

If the woman runs consistently at 8 mph, what is the speed of the train?

 

Solution to Problem:

The train travels at 32 mph.

If the jogger runs back 3/8ths of the length of the bridge, she will reach the beginning of the bridge just when the train does.

So, if she runs forward 3/8ths of the length of the bridge, she will be 6/8ths of the way across the bridge when the train reaches the beginning of the bridge.

This means the woman would run the last 2/8ths of the bridge in the time it would take the train to travel the whole 8/8ths of the bridge.

And so, the train must be traveling 4 times as fast as the jogger : 32 mph.


Correctly solved by:

1. David & Judy Dixon Bennettsville, South Carolina
2. Christopher March Virginia Tech, Blacksburg, Virginia
3. David Stark Winchester, Virginia
4. Walt Arrison Philadelphia, Pennsylvania
5. Nate Troup Arlington, Virginia
6. James Alarie University of Michigan -- Flint, Michigan
7. Nick von Keller Winchester, Virginia
8. Keith Mealy Cincinnati, Ohio
9. Richard Johnson La Jolla, California
10. Kirstine Wynn Winchester, Virginia
11. Justin Collins Winchester, Virginia
12. Geoff Keith Santa Monica, California
13. John Beasley Winchester, Virginia