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compartments that can be carried

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by sanju09 » Thu Jan 14, 2010 5:15 am
The speed of a railway engine is 42 miles per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 miles per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:
(A) 46
(B) 47
(C) 48
(D) 49
(E) 50
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by ace_gre » Thu Jan 14, 2010 12:24 pm
Hi, Here is my approach. I am not certain about my final answer though : ?

Max speed of the train w/o any compartments = 42.
Let the reduction in speed be S and n be the number of compartments.
also when speed =24, n=9.

Based on the relation, s = k * (n)^ 0.5
when speed = 24, reduction s= 42-24 = 18.
18= k * (9)^0.5 = 3k
k = 6.

n is max when S is atleast 41. I am assuming train has to move atleast 1mph.

41 = 6* (n)^0.5
(41/6) ^2 = n. If S=42, then n = 49. In which case train speed is 0. So I would go with C 48.
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