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speed, head start

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speed, head start

by francoisph » Wed Jun 23, 2010 5:32 am
A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10 th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30 th of a minute. What is B's speed in m/s?

(A) 12 answer

(B) 14

(C) 16

(D) 18

(E) 20
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by albatross86 » Wed Jun 23, 2010 5:38 am
Let A's speed be A m/s and B's be B m/s

First race. When A starts, B is already 48m into the race, but A still finishes 6 seconds before B
Thus : 480/A = 432/B - 6 ...1

Second race. When A starts, B is already 144m into the race, and A finishes 2 seconds after B.
Thus: 480/A = 336/B + 2 ...2

From 1 and 2:

432/B - 6 = 336/B +2
=> 96/B = 8
=> B = 12

Pick A
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by Rahul@gurome » Wed Jun 23, 2010 5:45 am
Let the Speed of A = X m/s and that of B = Y m/s
Then (480 - 48)/Y - 480/X = (1/10)(60) implies 432X - 480 Y = 6XY...Equation (1)
480/X - (480 - 144)/Y = (1/30)(60) implies 480Y - 336X = 2XY...Equation (2)
Solving the two equations we get Y = 12 m/s

The correct answer is (A).
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