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

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Manager
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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31 Oct 2008, 03:22
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

Thanks.

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

VP
Joined: 30 Jun 2008
Posts: 1034

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

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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

Thanks.

_________________

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

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

Current Student
Joined: 28 Dec 2004
Posts: 3350

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

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Schools: Wharton'11 HBS'12

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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
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

VP
Joined: 30 Jun 2008
Posts: 1034

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

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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

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

VP
Joined: 30 Jun 2008
Posts: 1034

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

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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 ..
_________________

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

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