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A and B stand at distinct points of a circular race track of length 12

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A and B stand at distinct points of a circular race track of length 12  [#permalink]

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New post 22 Oct 2019, 14:49
1
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

23% (04:36) correct 77% (03:41) wrong based on 13 sessions

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A and B stand at distinct points of a circular race track of length 120 meters. They run at speeds of 'a' meter per second and 'b' meter per second respectively. They meet for the first time 16 seconds after they started the race and for the second time 40 seconds from the time they started the race. If B had started in the opposite direction to the one he originally started, they would have met for the first time after 40 seconds. If B is quicker than A, find B’s speed (in meter per second).

A. 3
B. 4
C. 5
D. 8
E. 10

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Re: A and B stand at distinct points of a circular race track of length 12  [#permalink]

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New post 22 Oct 2019, 18:07
1
As the time taken by A and B to meet each other is less in real scenario than that in hypothetical one. Hence, they are moving towards each other in real scenario.

They will cover x distance to meet first time, and 120 to meet second time.

\(\frac{x}{a+b}=16\)......(1)

and

\(\frac{120}{a+b}\)=40-16.....(2)

From (1)and (2)

a+b=5, and x=80

Hypothetical situation
relative distance=120-80=40
relative speed= b-a

\(\frac{80}{b-a}=40\)
b-a=1

Hence, b=3 and a=2




DisciplinedPrep wrote:
A and B stand at distinct points of a circular race track of length 120 meters. They run at speeds of 'a' meter per second and 'b' meter per second respectively. They meet for the first time 16 seconds after they started the race and for the second time 40 seconds from the time they started the race. If B had started in the opposite direction to the one he originally started, they would have met for the first time after 40 seconds. If B is quicker than A, find B’s speed (in meter per second).

A. 3
B. 4
C. 5
D. 8
E. 10

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Intern
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A and B stand at distinct points of a circular race track of length 12  [#permalink]

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New post 22 Oct 2019, 22:26
since b is now running in opposite direction the gap between a and b is 120-x = 120 - 80 = 40.
b-a = 40/40
b-a = 1
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Re: A and B stand at distinct points of a circular race track of length 12  [#permalink]

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New post 22 Oct 2019, 23:02
I find the use of the word "race' in the question stem very confusing. In an actual race, contestants run in the same direction (usually clockwise), not in opposite directions.
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Re: A and B stand at distinct points of a circular race track of length 12   [#permalink] 22 Oct 2019, 23:02
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A and B stand at distinct points of a circular race track of length 12

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