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A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s?

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]

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12 Oct 2009, 09:35

1/10th of a minute = 6 seconds Similarly 1/30th of a minute is 2 seconds Also in first race A reaches before B whereas in second race B reaches before. Hence the order of equations

Re: A and B ran, at their respective constant rates, a race of 480 m. In [#permalink]

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24 Jul 2016, 06:07

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A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s?

(A) 12 (B) 14 (C) 16 (D) 18 (E) 20

Let \(x\) be the speed of B.

Write the equation:

(480-48)/x (time of B for first heat) - 6 (seconds, time B lost to A first heat) = TIME OF A (in both heats A runs with constant rate, so the time for first and second heats are the same)=(480-144)/x (time of B for second heat) + 2 (seconds, time B won to A second heat)

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