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.
=================================================================
**Jack's
solution:**
I did this very
differently than your formal solution
(mostly because
I was looking for a way to do it in my head):
If I run towards
the train I cover 3/8 the length of the bridge
just as the
train arrives. If I run the other way, I'm at the
3/8+3/8=3/4
point as the train arrives at the start. Therefore
I cover 1/4
of the bridge while the train covers the whole thing,
so the train
is moving 4x my speed => 60mph.
Thank you Jack.
I could not imagine how you could do this problem
without a solid
knowledge of at least Algebra II.
==================================================================
**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 1 of train
= time of man returning ( **Y / R = 3/8 (X) / 15**
)
and
Time 2 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.**
The only reason
I worked the problem was the site host's statement
that the problem
came from a 7th grade pre-algebra book. I would
be curious to
see how anyone worked the problem without knowing
Algebra II. |