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Race

by jerryragland » Sun Apr 25, 2010 5:36 pm
Source: Tough Problems (from resource section of this website)

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

[spoiler]ANS:12[/spoiler]
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by liferocks » Sun Apr 25, 2010 10:03 pm
Let A takes x minutes to cross 480m

so B takes x+6 minutes to cross 480-48 =432m
and B takes x-2 minutes to cross 480-144 =336m

now when speed is constant time is directly proportional with distance
hence
432:336 = (x+6): (x-2)
or 9:7= (x+6): (x-2)
or 9x-18=7x+42
or 2x=60
or x=30

hence B takes 36 minutes to cross 432m
speed of B is 432/36 m/s or 12m/s
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by rn4gmat » Sun Apr 25, 2010 10:19 pm
The Difference in the Distance is the two scenarios : 144-48 = 96 meters

The Difference in the tine in two scenarios : 1/10 min - ( -1/30 min) as B is beaten. = 8 Seconds

So Speed of B : 96/8 = 12 m/s

Hope this helps.
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