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A man cycling along the road

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A man cycling along the road

by georgepaul0071987 » Mon Jun 11, 2012 9:35 am
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

5 minutes
6 minutes
8 minutes
9 minutes
10 minutes
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by aneesh.kg » Mon Jun 11, 2012 10:00 am
georgepaul0071987 wrote:A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

5 minutes
6 minutes
8 minutes
9 minutes
10 minutes
Algebraic Approach:

Let B the speed of each bus and C the speed of the cyclist.

Let 'd' be the separation between consecutive buses and 't' be the time interval between consecutive buses.
Then d = B*t -- (1)

Relative speed of first bus and cyclist = B - C
d = (B - C)*12 -- (2)

Relative Speed of the oncoming bus and the cyclist = B + C
d = (B + C)*4 --(3)

Using (2) and (3),
B + C = 3*(B - C)
B = 2C

Substituting 'd' from (1) and B = 2C in (2),
B*t = (B - B/2)*12
[spoiler]t = 6 min[/spoiler]

[spoiler](B)[/spoiler] is the answer.
Aneesh Bangia
GMAT Math Coach
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