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the train kills him right (I)

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by sanju09 » Mon Mar 12, 2012 2:37 am
A straight rail subway, which is 8 meter long, has P and Q as its two openings. A man stands inside the subway 3 meter away from the opening P, when he notices a train about to enter the subway from the opening P. If the man, immediately after noticing the train, runs with his maximum speed towards the opening P, the train kills him right at the opening P; and if he immediately runs with his same maximum speed towards the opening Q, the train kills him right at the opening Q. How many times faster had been the train than the man?
(A) 2.5
(B) 3
(C) 3.5
(D) 4
(E) 4.5
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by killer1387 » Mon Mar 12, 2012 3:07 am
IMO D
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by goan81 » Mon Mar 12, 2012 10:24 pm
d = distance of the train from the opening P when the man first notices the train
r = speed of the train
m = speed of man

Equating the time required for the train and man to meet

1) d/r = 3/m

2) (d+8)/r = 5/m

d/3r = (d+8)/5r

solving the above equation gives d = 12

substituting for d in 1)

12/r = 3/m
gives

r = 4m

(D)
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