# Favorite Story Problem - No Algebra Required



## jaybird0827 (Feb 9, 2008)

A man is 3/8 of the way walking across a railroad trestle when he hears a train approaching at 60 mi/hr. If he runs to either end of the bridge, he can just make it to safety as the train passes. How fast does he have to run?


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## Semper Fidelis (Feb 9, 2008)

How long is the trestle?


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## Reformed Covenanter (Feb 9, 2008)

jaybird0827 said:


> A man is 3/8 of the way walking across a railroad trestle when he hears a train approaching at 60 mi/hr. If he runs to either end of the bridge, he can just make it to safety as the train passes. How fast does he have to run?



It would be safer to turn back.


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## Seb (Feb 9, 2008)

Very?


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## Wannabee (Feb 9, 2008)

jaybird0827 said:


> A man is 3/8 of the way walking across a railroad trestle when he hears a train approaching at 60 mi/hr. If he runs to either end of the bridge, he can just make it to safety as the train passes. How fast does he have to run?



Based on the information provided, as fast as he can.


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## Hilasmos (Feb 9, 2008)

How far away is a train when it is in hearing range?


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## Mushroom (Feb 9, 2008)

15 Mph


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## BJClark (Feb 9, 2008)

My husband says as fast as he can...

How high up is the trestle, and could he jump off the side as opposed to trying to outrun the train? Is there water or land under the trestle?


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## jaybird0827 (Feb 9, 2008)

SemperFideles said:


> How long is the trestle?


 
The actual distance does not matter. Brad got it right.


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## jaybird0827 (Feb 9, 2008)

Hilasmos said:


> How far away is a train when it is in hearing range?


 
The problem can be solved without that information. Brad solved it correctly.


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## jaybird0827 (Feb 9, 2008)

Brad said:


> 15 Mph


 
Right you are!


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## Seb (Feb 9, 2008)

Now wait a minute! He can't just answer 15 mph and that be it. 

I gave at least 3 minutes of thought and a couple of Google searches to it (which I'm suspecting that where somebody's *cough* *cough* Brad's answer come from)

Please explain and enlighten.


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## Mushroom (Feb 10, 2008)

Seb said:


> Now wait a minute! He can't just answer 15 mph and that be it.
> 
> I gave at least 3 minutes of thought and a couple of Google searches to it (which I'm suspecting that where somebody's *cough* *cough* Brad's answer come from)
> 
> Please explain and enlighten.



Nope. Done it in my head. 3/8 one way, 5/8 the other. Difference is 2/8 (1/4). I've gotta cover 1/4 the distance in the same time as the train, thus 1/4 the speed = 15 mph.


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## Seb (Feb 10, 2008)

Brad said:


> Seb said:
> 
> 
> > Now wait a minute! He can't just answer 15 mph and that be it.
> ...



OOooohhhh. Now I see.  Good job Brad. I don't think I would have never gotten that one.



jaybird0827 said:


> If he runs to either end of the bridge, he can just make it to safety as the train passes.



15 mph? That's a 4 minute mile. If this guy's like me then he's not going to "just make it to safety as the train passes" - HE'S GONNA DIE!!!  

I don't think I could run 15 mph for more than a couch length nowadays.

Great math problem Jay! I like the brain benders.


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## jaybird0827 (Feb 11, 2008)

> ...
> 15 mph? That's a 4 minute mile. If this guy's like me then he's not going to "just make it to safety as the train passes" - HE'S GONNA DIE!!!
> ...


 
Yeah, your right!



> ...
> Great math problem Jay! I like the brain benders.


 
Glad you enjoyed it.


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## smhbbag (Feb 11, 2008)

I'm not quite sure how subtracting 3/8 from 5/8 is relevant at all.

If the trestle is 1000 yards long, and the train is 1/4 mile away from the start of the trestle (our guy has bad hearing), then he will have to run 375 yards in 15 seconds, or 625 yards in just under a minute. Running 15 mph just ain't gonna cut it.

Or, the train could be 2 miles away (blowing his whistle real loud), and the trestle could be only 30 yards long. In that case, he can leisurely stroll to either side.

Just these two examples show the length of the trestle and the distance of the train are not optional information, In my humble opinion.


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## jaybird0827 (Feb 11, 2008)

smhbbag said:


> I'm not quite sure how subtracting 3/8 from 5/8 is relevant at all.
> 
> If the trestle is 1000 yards long, and the train is 1/4 mile away from the start of the trestle (our guy has bad hearing), then he will have to run 375 yards in 15 seconds, or 625 yards in just under a minute. Running 15 mph just ain't gonna cut it.
> 
> ...


 
It's just a math problem, and given the conditions in the problem, there is a unique solution.

You have to work with the given conditions, or those posed by the problem. The train is 3/8 of a bridge from the bridge.

The conditions that you describe lead to a different problem and a different solution.


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## smhbbag (Feb 11, 2008)

> The train is 3/8 of a bridge from the bridge.



Where does the problem say this?

It only says: 

"A man is 3/8 of the way walking across a railroad trestle when he hears a train approaching at 60 mi/hr." 

All we know about the train is its speed, and that the man can hear it when he is on the bridge.

There is no description of where the train is or how far away, relative to the trestle.

If the train is 3/8 of a trestle away from the trestle, then the problem is solvable with a unique solution. But that information wasn't given.


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## Mushroom (Feb 12, 2008)

smhbbag said:


> > The train is 3/8 of a bridge from the bridge.
> 
> 
> 
> ...



That information is given in that if he ran the shortest distance to get off the bridge, he would just make it off as the train got to the bridge. The train is as far away from the bridge as it would take to travel in the same time it would take the man to travel 3/8 of the length of the bridge.

Any distances you plug in have to take this into account. Example:

8 mile long bridge. Either direction the man travels, the train will reach the first side of the bridge when he has traveled 3 miles at the speed we're looking for. If he goes away from the train, there will be 2 miles left to go at the moment the train gets to the bridge. The man will have to traverse 2 miles in the same time the train goes 8 miles, which means he will have to move at 1/4 the speed of the train, or 15 MPH.

In this example the train would be 12 miles from the bridge when the man first hears it (pretty good hearing), or 12 minutes away in time. 12 minutes at 15 MPH comes to 3 miles. The train will always be 4 times the distance from the bridge as the man is from the closest side of the bridge, because it is established that the man will cover 1/4 the length of the bridge in the same time it will take the train to travel the entire length of it, and he is therefore traveling at 1/4 the speed.


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