## A lucky escape

Posted by Chris on December 11, 2010 – 7:12 pm

Two boys walking in the woods decided to take a shortcut through a railroad tunnel. when they had walked two-third of the way through the tunnel, their worst fears were realized. A train was coming from the opposite direction, nearing the tunnel entrance. The boys panicked and each ran for a different end of the tunnel. Both boys ran at the same speed, 10 miles per hour. Each boy escaped the tunnel just at the instant that the train would have squashed them into the rails.

Assuming the trains’ speed was constant, and both boys were capable of instantaneous reaction and acceleration, how fast was the train going ?

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I have solved this one. If I had done that earlier, I probably wouldn’t have bothered posting it.

December 11th, 2010 at 8:03 pm

30 mph! The boy running the longer length will still have 1/3 the distance to go when the other boy escapes. The train has to go 3 times the distance as the remaining boy in the same time span.

December 11th, 2010 at 8:15 pm

Hi nimble11. Your method of deducing the result is slicker than mine. Nicely done, and of course 30 mph is the right answer

December 12th, 2010 at 2:55 am

30 mp…… grrr

December 12th, 2010 at 10:02 pm

I did it by brute force (algebra).

2/3*L=10(L/V + L/30)

V = 30

December 15th, 2010 at 7:35 pm

V(train)=5

December 18th, 2010 at 11:05 am

velocity of train must be 30 miles per hour…..

let there are two boys, say A,B.

A has to cover 1/3rd distance and takes time t.In the mean while train enters the tunnel, and boy B travels 1/3rd distance(Know he has two travel 1/3rd more).

Therefore if boy B takes t time, he covers 10t distance and the train covers 30t distance(since B starts with A, A travels 10t, remaining 20t traveled by B). hence speed of train is 3 times the speed of boy…

i.e speed of train is 30miles/hours

December 19th, 2010 at 2:17 pm

20 mph

i say

what do you thiink?

December 19th, 2010 at 5:04 pm

Hi Noah. Why do you say 20 mph?

December 19th, 2010 at 8:55 pm

its simple its 30mph

September 5th, 2012 at 2:56 am

15mph is ur speed

bt i not conform what u think…???