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

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Manager
Joined: 16 Oct 2008
Posts: 54
A and B ran a race of 480 m. In the first heat, A gives B a [#permalink]

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28 Oct 2008, 05:52
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

6.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
Director
Joined: 14 Aug 2007
Posts: 704

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28 Oct 2008, 07:25
Natasha0123 wrote:
6.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

1/10th of minute = 6 sec
1/30th of minute = 2 sec

First heat:
tA = tB - 6 (in seconds)

tA = 480/RA
tB = (480 - 48)/RB

Therefore:
480/RA = 432/RB - 6.... (x)

Second heat:
tA = tB + 2 (in seconds)

tA = 480/RA
tB = 336/RB

480/RA = 336/RB + 2.... (y)

96m/8s = 12 m/s = RB
Director
Joined: 23 May 2008
Posts: 760

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28 Oct 2008, 10:41
R*T=D

heat 1
A) RT=480
B) R(T-6)=480-48=432

heat 2
A) RT=D
B) R(T-2)=480

you can deduce that

432/t-6 = 480/t-2
t=42

rate for B =432/(42-6) = 12
VP
Joined: 05 Jul 2008
Posts: 1378

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28 Oct 2008, 12:27
(432/y) - (480/x) =6 because B took more time to finish

(480/x) - (336/y) = 2 because A took more time to finish

Add them up 96/y =8 means y =12
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# A and B ran a race of 480 m. In the first heat, A gives B a

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