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A locomotive engine without a train can run at 24mph. The

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Joined: 20 Dec 2004
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A locomotive engine without a train can run at 24mph. The [#permalink]  12 Oct 2005, 20:11
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A locomotive engine without a train can run at 24mph. The speed diminishes by a quantity which varies as the square root of the number of wagons attached. With 4 wagons the speed is 20mph. The greatest number of wagons that the engine can move is...

A. 195
B. 143
C. 120
D. 24
E. 20
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Joined: 21 Aug 2005
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B. 143

Let x be the factor by which the speed decreases.
x proportional to sqrt(wagons)
x = Kw, k is a constant and w=wagons.
From the Q, the speed decreases by 4 (x) with 4 wagons,
so 4 = k*sqrt(4) => k=2

If the speed reduces by 24, the engine cannot move. At this condition,
24=2*sqrt(w) => w=144. So when there are 144 wagons, the engine cannot move. With 143 wagons, it can and that is the max.
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