Frank is walking across a one mile long railroad bridge ignoring his mother's commands and the signs on the bridge. He has
walked 1/4 of a mile when he looks back and sees a train coming. The train is 3/4 of a mile from the beginning of the bridge.
Which way should he run?
Let F = speed of Frank and let T = rate of the train.
Determine the answers to the following questions:
(1) What relationship between F and T would make running
(a) toward the train appropriate?
(b) away from the train appropriate?
(2) What relationship between F and T corresponds to
(a) his escaping in both directions?
(b) his escaping in neither direction?
Be complete and show your work.
Solution to the Problem:
(1a) F > (1/3) T(1b) F > (3/7) T
(2a) F > (3/7) T
(2b) F < (1/3) T
If Frank runs toward the train, it will take him 1/(4F) hour to get off the bridge (1/4 mile / F mph)
Meanwhile, it will take the train 3/(4T) hour to get to the bridge (3/4 mile / T mph).
Set these equal to get 3F = T or F = (1/3) T.
So Frank should run toward the train when F > (1/3) T.
If Frank runs away from the train, it will take him 3/(4F) hour to get off the bridge (3/4 mile / F mph)
Meanwhile, it will take the train 7/(4T) hour to get to the bridge (7/4 mile / T mph).
Set these equal to get 7F = 3T or F = (3/7) T.
So Frank should run away from the train when F > (3/7) T.
Correctly solved by:
| 1. Colin (Yowie) Bowey | Beechworth, Victoria, Australia |
| 2. Veena Mg | Bangalore, Karnataka, India |
| 3. Ivy Joseph | Pune, Maharashtra, India |
| 4. Pearl Burruss |
Delta High School, Delta, Colorado |