December 2020
Problem of the Month

Railroad Bridge Part 2

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

Send any comments or questions to: David Pleacher