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A and B ran a race of 480 m. In the first heat, A gives B a head start

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A and B ran a race of 480 m. In the first heat, A gives B a head start [#permalink] New post   09 Nov 2022, 06:24
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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 1/10th 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


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A
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Re: A and B ran a race of 480 m. In the first heat, A gives B a head start [#permalink] New post   14 Nov 2022, 07:31
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1. Distance of B = 432
if A takes t mins, B takes = (t + 1/10)

2. Distance of B = 336
if A takes t mins, B takes = (t - 1/30)

Therefore to run (432 - 336) = 96 m , B took time (1/30 + 1/10)

i.e 96 = (1/30 + 1/10) * Speed of B

This is the speed of B in m/min. Dividing by 60, speed of B in m/sec = 12.

Answer: A
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Re: A and B ran a race of 480 m. In the first heat, A gives B a head start [#permalink] New post   18 Dec 2023, 03:31
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Let speed of B x and speed of A be y

If A has head start of 48m so distance run by B = 432m

A will run 480m


432/x - 480/y = 6

Second phase B has a head start of 144m


480/y - 336/x = 2


Therefore

432y - 480x = 6xy

-336y + 480x = 2xy


96 y= 8xy

x = 12m/s

Adewale Fasipe, GRE quant instructor from Nigeria
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Re: A and B ran a race of 480 m. In the first heat, A gives B a head start [#permalink]
18 Dec 2023, 03:31
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