train kills him

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train kills him

by sanju09 » Mon Feb 22, 2010 4:54 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 ajith » Mon Feb 22, 2010 5:02 am
sanju09 wrote: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
Say, Initially the train was x meters away from the Entrance P and it runs m times faster than the man

x/m = 3 ( the man runs 3 meters; the train would have run x meters in the same time)

x= 3m

(x+8)/m = 5 (man runs 5 m; at the same time train runs x+8 meter)

x+8 = 5m

x/(x+8) = 3/5

x= 12
[spoiler]m = 4, D
[/spoiler]
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