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Bus & cycle

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by crackgmat007 » Sat Sep 26, 2009 10:42 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
8
9
10

OA - B
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Re: Bus & cycle

by fruti_yum » Wed Sep 30, 2009 9:43 am
crackgmat007 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
8
9
10

OA - B
Dont know what consecutive buses are.. are these oncoming or going buses? the question seems too vague.. what is the source?
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by crackgmat007 » Thu Oct 01, 2009 6:57 pm
GMAT club
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by vaibhav.iit2002 » Fri Oct 02, 2009 4:30 am
here all buses are coming at same speed - from both directions

let say speed of bus=b, speed of cycle=c, time interval bet. consecutive buses=t

now if cycle wasn't moving and distance between first bus and cycle=s, then

s=bxt ...1
now when cycle is moving, its relative speed for an upcoming bus will be b+c and that for the other direction bus will be b-c

now s=(b+c)x4 and s=(b-c)x12

solving these eq, b=2c => s=3bx4/2=6b

from 1, bxt=s=6b, hence t=6

Ans. B
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