SOLUTION: You are walking across a rail bridge, and are 3/8 of the way across. You hear a train approaching behind you at 60 miles per hour. You do some quick calculation,

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Question 204382: You are walking across a rail bridge, and are 3/8 of the way across.

You hear a train approaching behind you at 60 miles per hour.

You do some quick calculation, and you realize that you can either run back or forward, and either way, you can make it to the end of the bridge and get off the tracks, just in time to avoid getting hit by the train. That is, you will get to the end of the bridge (either behind you or in front of you) the exact same time as the train.

What is your running speed?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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:
You are walking across a rail bridge, and are 3/8 of the way across.
You hear a train approaching behind you at 60 miles per hour.
You do some quick calculation, and you realize that you can either run back
or forward, and either way, you can make it to the end of the bridge and get
off the tracks, just in time to avoid getting hit by the train.
That is, you will get to the end of the bridge (either behind you or in front
of you) the exact same time as the train.
What is your running speed?
:
Train----------d------------Br.....3x......Y..........5x.........Br
:
Let d = dist train is from the bridge
Let 8x = length of the bridge
You (Y) are 3x from one end and 5x from the other end of the bridge
:
Let s = running speed (mph)
:
Toward the train time equation (arrive at end of the bridge at the same time)
Train time = your time
d%2F60 = %283x%29%2Fs
Cross multiply:
ds = 60(3x)
ds = 180x
d = %28180x%29%2Fs
:
Away from the train time equation (arrive at other end at the same time)
%28%28d%2B8x%29%29%2F60 = %285x%29%2Fs
Cross multiply
s(d+8x) = 60(5x)
s(d+8x) = 300x
d + 8x = %28300x%29%2Fs
Replace d with %28180x%29%2Fs (from the 1st equation)
%28180x%29%2Fs + 8x = %28300x%29%2Fs
Get rid of x, divide thru by x and you have:
180%2Fs + 8 = 300%2Fs
Multiply by s:
180 + 8s = 300
8s = 300 - 180
8s = 120
s = 120%2F8
s = 15 mph running speed
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