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Tuesday puzzle

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Tuesday puzzle

#1

Tuesday puzzle

Alex Y

You are walking across a railroad trestle and when 3/8 of the way across, hear a train whistle coming from behind. In an instant, you weigh your options of running back toward the near end versus running away from the train, make your decision, and run. As it turns out, it didn't make any difference which way you ran; either way you would clear the trestle just before being hit. If you can run 10 mph, how fast was the train moving?

Part II: I solved the above with algebra. It was pretty straightforward. But there is another approach (which I guess is implicitly algebra, but you don't really have to assign any variables or write down any formulas) that you can do in your head. Can you find that reasoning/solution?

Re: Tuesday puzzle

#2

Re: Tuesday puzzle

Larry Barrett

In time T1, the train travels a distance X at a rate R.

In the same time T1, the man runs a distance 3/8 B (the length of the bridge) at a rate 10mph.

In time T2, the train travels a distance X + B at a rate R.

In the same timeT2, the man runs a distance 5/8 B at a rate 10mph.

So consider the difference in time T2-T1. The train goes a distance (X+B)- X = B while the man travels a distance (5/8 B) - (3/8 B)= 1/4 B. So the train must travel at a rate 4 times the man's rate = 40mph.

Re: Tuesday puzzle

#3

Correct algebraic solution

Alex Y

Now, can you see it without the variables? Hint--your last paragraph contains the essence of this version.

Re: Tuesday puzzle

#4

Re: Correct algebraic solution

Larry Barrett

In the first case, when the man has run 3/8 B toward the beginning of the bridge, the train has traveled a distance X toward the bridge, reaching the beginning of the bridge at the same time.

In the second case, the man runs a total distance 5/8 B toward the end of the bridge. When he has run 3/8 of that distance, the train has again reached the beginning of the bridge (based on the first case). When the man runs the remaining 2/8 B (=1/4 B) to the end of the bridge, the train goes the whole distance B, reaching the end at the same time. So the train must travel at a speed 4 times the man to travel 4 times the distance in the same time. Hence train speed is 40mph.

Re: Tuesday puzzle

#5

That's it

Alex Y

Another way of looking at it is to imagine you were walking with a friend who runs the same speed as you. Your friend runs back toward the train while you run away. At the point where the train reaches the bridge, you both will have run 3/8 of the length of the bridge, which will put you 3/4 of the way across. You run that final 1/4 in the same time as it takes the train to cross the whole trestle.

None of those dreaded variables! (at least none explicit)

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