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Topic: Man Vs. Train (Read 10706 times) |
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Jeremy
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"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."
i split the bridge into 8 section.
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if the man were to run from his section to the start of the bridge it would take him 3 units of time. and the train would get there at the same time. So if the man runs the other way in 3 units of time (just as he passes the 6th section) the train will enter the track. so the man has to cover 2 units of track, and in the same amount of time the train has to cover 8. so the train is moving 4 times faster than the man, so 60mph
all i gatta say is this guy must be a track star if he can run a 4 minute mile.
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Chronos
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Re: Man Vs. Train
« Reply #1 on: Sep 15th, 2002, 10:10pm » |
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Nobody ever said that he's running a four minute mile. He's sprinting at 15 mph, which is a much different matter.
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unicorn
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Well I have to agree with Jeremy. The answer is 60mph. But the man need not sprint at 4 minute. With the given speed he can still make it. 
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ashutoshets
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Re: Man Vs. Train
« Reply #3 on: Feb 23rd, 2012, 11:12pm » |
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Well I have to agree with Jeremy. The answer is 60mph. But the man need not sprint at 4 minute. With the given speed he can still make i
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frankrizal
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Re: Man Vs. Train
« Reply #4 on: Feb 28th, 2012, 1:41am » |
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My answer would be 45 mph.  No explanation, just an answers. har har
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iatkrox
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Re: Man Vs. Train
« Reply #5 on: Jul 2nd, 2012, 12:47am » |
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hmmm I agree with Chronos and my guess is 50mph 
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webtasarim
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Re: Man Vs. Train
« Reply #6 on: Oct 6th, 2013, 4:27pm » |
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between 50-60
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UgoLocal02
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Re: Man Vs. Train
« Reply #7 on: Jun 12th, 2014, 2:23am » |
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50-60
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EdwardSmith
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Re: Man Vs. Train
« Reply #8 on: Jul 7th, 2014, 12:33pm » |
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It depends on how long the bridge is.
If its a long bridge he wont make it.
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towr
wu::riddles Moderator
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Re: Man Vs. Train
« Reply #9 on: Jul 7th, 2014, 9:55pm » |
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on Jul 7th, 2014, 12:33pm, EdwardSmith wrote:It depends on how long the bridge is.
If its a long bridge he wont make it. |
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Yes he will, because it's in the problem statement that he does barely make it.
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Wikipedia, Google, Mathworld, Integer sequence DB
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EdwardSmith
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Re: Man Vs. Train
« Reply #10 on: Jul 8th, 2014, 3:45am » |
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Yes you are right.
But I think Ive solved it.
My limited mathematical knowledge has done the calculation this ridiculous way.
Lets assume that it is an enormous bridge that stretches for 120 miles.
Each 1/8th section would then measure 15 miles each.
So it would take the man 3 hours to reach the end of the bridge.
In order for the train to reach the man in 3 hours it would have to be travelling at 40mph.
So thats the answer 40mph.
I suppose that you can scale down the size of the bridge to come up with the same answer.
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rmsgrey
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Re: Man Vs. Train
« Reply #11 on: Jul 8th, 2014, 6:58am » |
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on Jul 8th, 2014, 3:45am, EdwardSmith wrote:Yes you are right.
But I think Ive solved it.
My limited mathematical knowledge has done the calculation this ridiculous way.
Lets assume that it is an enormous bridge that stretches for 120 miles.
Each 1/8th section would then measure 15 miles each.
So it would take the man 3 hours to reach the end of the bridge.
In order for the train to reach the man in 3 hours it would have to be travelling at 40mph.
So thats the answer 40mph.
I suppose that you can scale down the size of the bridge to come up with the same answer. |
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You seem to have answered a different question, where the train is at the far end of the bridge and the man can just barely reach the near end before the train catches him.
The original question has the train reaching the near end of the bridge at the same time as the man if he runs that way, or the far end at the same time as the man if he runs that way, so the train is an unknown distance from the bridge, approaching from the nearer end.
On your sample bridge, it takes him 3 hours to reach the near end (just as the train does) or 5 hours to reach the far end (just as the train does)
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EdwardSmith
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Re: Man Vs. Train
« Reply #12 on: Jul 12th, 2014, 2:38am » |
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I will have another crack at this one.
The train is travelling 4 times as fast as the man.
Therefore if the man will run 3 units in the time it takes the train to cover 12 units.
So the train is 7 units from the start of the bridge when the man see it.
Or have I misunderstood the question yet again.
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| « Last Edit: Jul 12th, 2014, 2:40am by EdwardSmith » |
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rmsgrey
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Re: Man Vs. Train
« Reply #13 on: Jul 12th, 2014, 5:10am » |
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on Jul 12th, 2014, 2:38am, EdwardSmith wrote:I will have another crack at this one.
The train is travelling 4 times as fast as the man.
Therefore if the man will run 3 units in the time it takes the train to cover 12 units.
So the train is 7 units from the start of the bridge when the man see it.
Or have I misunderstood the question yet again. |
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Let's call the near end of the bridge 0, the man's current position 3, and the far end 8. Then the train starts at -T and will take the same length of time to reach each end of the bridge as the man would, so, looking at times to reach the near end: T/v=3/15; and the far end: (T+/v=5/15.
Solving that system of equations gives a value for T and a value for v (it may be worth pointing out that, while v is in mph, T is in unknown units, but that's a detail).
From the train being 4 times the speed of the man (which is what the question asks you to find out) you do indeed get that the train travels 12 units while the man travels 3, but that puts them both at the near end of the bridge, meaning the train starts 12 units from one end of the bridge (and 20 from the other)
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bekatcho
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Re: Man Vs. Train
« Reply #14 on: Jul 13th, 2014, 12:45pm » |
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i think it will be 50 miles
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riddler358
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Re: Man Vs. Train
« Reply #15 on: Sep 13th, 2014, 12:14pm » |
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It's almost 60
Assume they just meet at the beginning and at the end for easy calculation
By the time man runs 3/8 train is at the beginning
By the time man runs 5/8 train is at the end
Train goes through whole bridge at the same time as man goes through 2/8
Therefor train is 4 times faster than man
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