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A railroad worker finds himself trapped inside a tunnel at a point

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A railroad worker finds himself trapped inside a tunnel at a point  [#permalink]

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New post Updated on: 12 Sep 2017, 19:16
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Difficulty:

  95% (hard)

Question Stats:

34% (03:52) correct 66% (04:01) wrong based on 71 sessions

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A railroad worker finds himself trapped inside a tunnel at a point that is 25% of the length of the tunnel with a train approaching towards the near end with constant speed. He calculates that if he runs towards the near end doubling his speed then he would just manage to save himself. If on the other hand, he reduced his speed by 25% and ran towards the far end of the tunnel, then he would also just manage to avert danger. What is the the ratio of the speed of the train to the speed of the worker?
(1) 8 : 7
(2) 7 : 8
(3) 3 : 1
(4) 2 : 1
(5) None of these

Originally posted by theperfectgentleman on 12 Sep 2017, 10:51.
Last edited by theperfectgentleman on 12 Sep 2017, 19:16, edited 1 time in total.
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Re: A railroad worker finds himself trapped inside a tunnel at a point  [#permalink]

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New post 12 Sep 2017, 11:31
Let length of tunnel be - x
Let distance of train from nearest end be - y
Let speed of man be - m
Let speed of train be - t

Condition 1 : when the man runs to the nearest end of tunnel
To be just in time we can write the equation as

y/t = [25x]/[100*(2m)]
or y = xt/8m ..........eq (1)

Condition 2 : When the man runs to the further end of the tunnel
To be just in time we can write the equation as

(y+x)/t = [75x/100]/[75m/100]

On simplifing we get

y = (xt/m) - x .........(eq 2)

equating eq 1 and eq 2 we get

xt/8m = (xt/m) - x
simpliying we get

t/m = 8/7

Hence answer is A
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Re: A railroad worker finds himself trapped inside a tunnel at a point  [#permalink]

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New post 12 Sep 2017, 11:33
theperfectgentleman wrote:
A railroad worker finds himself trapped inside a tunnel at a point that is 25% of the length of the tunnel with a train approaching towards the near end with constant speed. He calculates that if he runs towards the near end doubling his speed then he would just manage to save himself. If on the other hand, he reduced his speed by 25% and ran
towards the far end of the tunnel, then he would also just manage to avert danger. What is the the ratio of the speed of the train to the speed of the worker?
(1) 8 : 7
(2) 7 : 8
(3) 3 : 1
(4) 2 : 1
(5) None of these


rt=rate of train
rw=rate of worker
d=distance from engine to tunnel
t=distance of tunnel
equation1: d/rt=(t/4)/2rw➡
rt/rw=8d/t
equation2: (d+t)/rt=(3t/4)/(3rw/4)➡
rt/rw=t+d/t
8d/t=(t+d)/t➡
8d=t+d➡
t=7d
rt/rw=t+d/t=8d/7d=8:7
(1)
Re: A railroad worker finds himself trapped inside a tunnel at a point &nbs [#permalink] 12 Sep 2017, 11:33
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