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A man cycling along the road noticed that every 12 minutes a

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Joined: 14 Oct 2008
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A man cycling along the road noticed that every 12 minutes a [#permalink]

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New post 31 Oct 2008, 03:22
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A man cycling along the road noticed that every 12 minutes a bus overtakes him while every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at constant speed, what is the time interval between consecutive buses?

5 minutes
6 minutes
8 minutes
9 minutes
10 minutes

Please explain your approach while answering.
Thanks.

Kudos [?]: 64 [0], given: 0

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Kudos [?]: 708 [0], given: 1

Re: bus and cycle [#permalink]

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New post 31 Oct 2008, 07:02
gameCode wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him while every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at constant speed, what is the time interval between consecutive buses?

5 minutes
6 minutes
8 minutes
9 minutes
10 minutes

Please explain your approach while answering.
Thanks.


Already posted here : http://gmatclub.com/forum/7-t69862
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Location: New York City
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Re: bus and cycle [#permalink]

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New post 31 Oct 2008, 07:53
gameCode wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him while every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at constant speed, what is the time interval between consecutive buses?
5 minutes
6 minutes
8 minutes
9 minutes
10 minutes
Please explain your approach while answering.
Thanks.


lets see D=Distance, Vb=Speed of Bus and Vm=Speed of cyclist

D/(vb-vm)=12
D/(Vb+vm)=4

we want to know D/Vb

do D=(vb-vm)12

(vb-vm)/(vb+vm)=3

solve you get Vm=Vb/2

now sub

D/(vb-vm)=D/(vb-1/2vb)=12/2 or 6

Kudos [?]: 319 [0], given: 2

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Re: bus and cycle [#permalink]

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New post 31 Oct 2008, 22:14
fresinha12 wrote:
gameCode wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him while every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at constant speed, what is the time interval between consecutive buses?

5 minutes
6 minutes
8 minutes
9 minutes
10 minutes

Please explain your approach while answering.
Thanks.


lets see D=Distance, Vb=Speed of Bus and Vm=Speed of cyclist

D/(vb-vm)=12
D/(Vb+vm)=4

we want to know D/Vb

do D=(vb-vm)12

(vb-vm)/(vb+vm)=3

solve you get Vm=Vb/2

now sub

D/(vb-vm)=D/(vb-1/2vb)=12/2 or 6


fresinha ... just to ensure what I have understood is right
D/(vb-vm)=12 ----- > here we do (Vb-Vm) just because the bus and the man are traveling in same direction. right ?
D/(Vb+vm)=4 ------ > here (Vb+Vm) because the bus and man are traveling in the opposite direction. right ?

Also, why do we have the same distance D for all instances ? and I do not understand how D/Vb is the time interval between the two buses .....

I would appreciate any help :)

Thanks
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Kudos [?]: 708 [0], given: 1

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Joined: 30 Jun 2008
Posts: 1034

Kudos [?]: 708 [0], given: 1

Re: bus and cycle [#permalink]

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New post 01 Nov 2008, 09:29
fresinha12 wrote:
fresinha ... just to ensure what I have understood is right
D/(vb-vm)=12 ----- > here we do (Vb-Vm) just because the bus and the man are traveling in same direction. right ?YES
D/(Vb+vm)=4 ------ > here (Vb+Vm) because the bus and man are traveling in the opposite direction. right ?YES

Also, why do we have the same distance D for all instances ? and I do not understand how D/Vb is the time interval between the two buses .....

we are told that buses run on constant interval that means all buses run at the same speed, thus the time apart is simply the time it takes a bus to travel distance D. D is the distance the cyclist travelled when the first bus passed him until he meets the oncoming bus

I would appreciate any help :)

Thanks


I get it now :) Thanks a lot ..
_________________

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Kudos [?]: 708 [0], given: 1

Re: bus and cycle   [#permalink] 01 Nov 2008, 09:29
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