Subj: MATH PROB. - Train Bridge (S447b)
From: William Wu of U. C. Berkeley
At: http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml
Source: http://www.ocf.berkeley.edu/~wwu/riddles/easy.shtml#trainBridge
A man is 3/8's of the way across a train bridge, when he
hears the whistle of an approaching train behind him. It
turns out that he can run in either direction and just
barely make it off the bridge before getting hit. If he
is running at 15 mph, how fast is the train traveling?
Assume the train travels at a constant speed, despite
seeing you on the tracks.
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My solution:
Let X = the width of the bridge
and
Y = the distance the train is from the bridge at the start
and
R = the rate of the train
Distance equals Rate times Time ( D = R x T )
or
Time equals Distance divided by Rate ( T = D/R )
Therefore
Time of train = time of man returning ( Y / R = 3/8 (X) / 15 )
and
Time of train = time of man going forward ( (Y + X)/R = 5/8 (X) / 15 )
That's two equations and three unknowns, but it solves.
Cross multiplying yields
15 Y = 3/8 X R and 15 Y + 15 X = 5/8 X R
Substitute the 15 Y from the first equation into the second yields
3/8 X R + 15 X = 5/8 X R
Divide everywhere by X.
3/8 X + 15 = 5/8 X
15 = 1/4 X
60 mph = X
The train is going 60 mph no matter the width of the bridge.
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