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Railroad Bridge question...

Having resorted to high school mathematics, I finally came up with the answer that the train is twice as fast as the man.

Using time = distance/speed

we know that the time for the man to get to two different points is the same as the corresponding times it takes the train to reach the same points, albeit different distances.

Anyone else get the same answer?

Sook
Tuesday, June 29, 2004

Right, the train is twice as fast as the man.
Here's why:
Say Y the distance between the train and the tunnel entrance.
Say X the distance between the man and the tunnel entrance.
The tunnel is 4X long.
Since (case 1: man runs back):

Y = train speed * elapsed time (case1);
X = man speed * elapsed time (case1);

and being the elapsed time the same for both:

train speed / man speed = Y/X

but we have also (case 2: man keeps running)


Y+4X = train speed * elapsed time (case2);
3X = man speed * elapsed time (case2);

and being the elapsed time the same for both:

train speed / man speed =(Y+4X)/3X

so:
Y/X = (Y+4X)/3X --> Y=2X --> train speed = 2 * man speed

michele
Wednesday, June 30, 2004

This is an Easy one.

Let t,m represent the speed of train and man.
Also assume the distance between the train and turnnel is a and the lenght of the turnel is b, then we have the following two equations:

if man runs backword we have:
a/t = b/4m    (1)

if man runs forward we have:
(a+b)/t = 3b/4m  (2)

solve (1) for a we get:  a=bt/4m  (3)

substitute (3) into (2)

(bt/4m +b)/t = 3b/4m

Multiply t/b on both side:
t/4m +1 = 3t/4m

solve for t/m we get

t/m=2

So the train's speed is twice as fast as the man's.

Steve Li
Thursday, July 01, 2004

When interviewers ask this type of question, there is usually a clever way to solve it without using mathematical equations. Here is a solution in simple english:

It says that if the man runs back to the start of the tunnel, the train hits him. If instead, he runs the opposite way, he will be exactly half way across the tunnel while the train will be at the beginning of the tunnel (a).

Now the second part says that if the man runs to the end of the tunnel, the train will hit him right at that spot (b).

Now combining (a) followed by (b), the man ran half the distance of the tunnel in the same time the train went the full distance of the tunnel. Thus, the train is twice as fast. :)

MJ
Friday, July 02, 2004

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