A man cycling

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kaulnikhil: Master | Next Rank: 500 Posts; Posts: 338; Joined: Fri Apr 17, 2009 1:49 amFollowed by: 3 members; Thanked: 9 times

by kaulnikhil » Thu Feb 25, 2010 1:12 pm

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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Source: Beat The GMAT — Problem Solving | Thu Feb 25, 2010 1:12 pm

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Thu Feb 25, 2010 2:00 pm

kaulnikhil 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

Let the speed of cyclist be C and bus be B.
Using the concept of relative speed:-
For incoming bus,speed = B + C
For overtaking bus,speed = B - C
Now,distance travelled b/w 2 incoming bus = (B + C)*4
Now,distance travelled b/w 2 overtaking bus = (B - C)*12
For every bus that overtakes,3 buses are incoming.
I am stuck now

Can anyone help??

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Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

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firdaus117: Master | Next Rank: 500 Posts; Posts: 102; Joined: Sat Feb 20, 2010 5:38 am; Location: IIM Ahmedabad; Thanked: 10 times

by firdaus117 » Sat Feb 27, 2010 1:26 pm

harsh.champ wrote: Let the speed of cyclist be C and bus be B.
Using the concept of relative speed:-
For incoming bus,speed = B + C
For overtaking bus,speed = B - C
Now,distance travelled b/w 2 incoming bus = (B + C)*4
Now,distance travelled b/w 2 overtaking bus = (B - C)*12
For every bus that overtakes,3 buses are incoming.
I am stuck now
Can anyone help??

Of course!!!
First comprehend this flawed question.It asks you the time interval between two consecutive buses running in the same direction.The question doesn't state this explicitly though as people may end up calculating duration between one bus that overtakes the cyclist and one that crosses him.Also,as all buses and the cyclist have constant speed and as any two buses start with same time gap,we can cosider them equal(again not stated explicitly in the question)
so,
(B + C)*4 = (B - C)*12
or, B=2C
Hence,distance b/w two buses in same direction,d=4*(3/2)B=6 B
Therefore, time gap=d/B=6 minutes

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