Wizard
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Wizard
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July 4th, 2012 at 1:15:34 PM permalink
You are 40% of the way across a train bridge when you hear a train whistle behind you. You must choose to turn around or keep going forward to get off the bridge before the train runs you over. It turns out that regardless of which way you choose you will get off the bridge just in the knick of time. You can run 10 miles per hour. How fast is the train going?

As usual, please put solutions in
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Nareed
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July 4th, 2012 at 1:28:08 PM permalink
Quote: Wizard

You are 40% of the way across a train bridge when you hear a train whistle behind you. You must choose to turn around or keep going forward to get off the bridge before the train runs you over.



If the whistle, along with the attached train, is behind you, wouldn't it run you over sooner if you turned around?

Random guess:
40 mph
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Doc
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July 4th, 2012 at 2:18:03 PM permalink
Quote: Nareed

If the whistle, along with the attached train, is behind you, wouldn't it run you over sooner if you turned around?


Yes, if it were going to run over you both ways, that would happen sooner if you turned back. But depending on speeds and where you are on the bridge, there may be reversing answers on which direction is better. In this case, they are equally marginal.

X = length of bridge
t1=time until train reaches bridge
t2=time until train has crossed bridge
S=train speed

t1=(0.4X/10)
t2=(0.6X/10)
t2-t1=X/S

0.6X/10 - 0.4X/10 = 0.2X/10 = X/S
S =10/0.2 = 50 mph
Nareed
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July 4th, 2012 at 2:23:02 PM permalink
Quote: Doc

Yes, if it were going to run over you both ways, that would happen sooner if you turned back. But depending on speeds and where you are on the bridge, there may be reversing answers on which direction is better. In this case, they are equally marginal.



Ok.

BTW, your spoiler label shows the result.
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Ibeatyouraces
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July 4th, 2012 at 2:31:23 PM permalink
deleted
DUHHIIIIIIIII HEARD THAT!
Doc
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July 4th, 2012 at 2:31:41 PM permalink
Quote: Nareed

Ok.

BTW, your spoiler label shows the result.


I know. I thought we were supposed to hide the solution, i.e. the how to figure it out, not the answer. If I misunderstood, I apologize.
Wizard
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Wizard
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July 4th, 2012 at 5:08:32 PM permalink
Quote: Doc

I know. I thought we were supposed to hide the solution, i.e. the how to figure it out, not the answer. If I misunderstood, I apologize.



You're fine. I asked that only solutions be hidden. I figured nobody had to believe your answer, but I think in your case, Doc, everyone does.
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ThatDonGuy
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July 4th, 2012 at 5:15:32 PM permalink
Let L be the distance across the bridge you are when you hear the whistle. Since it is 40% of the way across the bridge, either you must turn around and run distance L, or keep going and run distance 1.5 L.

Let T be the distance the train is from the start of the bridge, and X be its velocity.
It takes you L/10 hours (if T is in miles) for you to reach the start of the bridge; it takes the train L/X hours (if L is in hours and X is in MPH) to get there. Therefore, L/10 = T/X.
It takes you 1.5 L/10 hours for you to reach the end of the bridge; it takes the train (T + 2.5L)/X hours. Therefore, 1.5 L/10 = (T + 2.5L)/X.
L/10 = T/X, so 1.5 L/10 = 1.5 T/X
1.5 T/X = (T + 2.5L)/X
1.5 T = T + 2.5 L
T = 5L
Substituting for T in L/10 = T/X, we get L/10 = 5L/X, so X = 50.
The train's velocity is 50 MPH.
ahiromu
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July 4th, 2012 at 5:28:29 PM permalink


L: Length of the bridge

You can get .4*L on the bridge before the train reaches said bridge. That means if you continue walking in the same direction as the train, you'll reach .8*L. In other words, in the time it takes you to run .2*L the train covers the entire length L... so the train is five times faster than you or 50 mph.



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P90
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July 4th, 2012 at 5:52:12 PM permalink
Let bridge span be L, with L1 distance to the train.
Let train velocity be v.
Don't click the spoiler until reading the rest of the post.

At the moment you hear the whistle (t1), the train has traveled L1*v/c, c=340
At the moment you are being run over as you are exiting the bridge (t2), the train has traveled L1*v/340+v*.6L/4.4704
At the moment you run into the train as you backpedal, the train has traveled L1*v/340+v*.4L/4.4704
These are separated by the bridge: L1*v/340+v*.4L/4.4704+L=L1*v/340+v*.6L/4.4704
.4Lv/4.4704+L-.6Lv/4.4704=0
-.2Lv/4.4704=-L
Lv=L*4.4704/.2
v=22.352 (same answer)

I hoped the additional factor would play some role, or you could determine L, but it's as straightforward as it looks, I can't see any trick if there should be one.
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