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PS-Velocity (Must try)

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PS-Velocity (Must try) [#permalink]

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New post 01 Jun 2009, 02:01
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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

Can someone explain what is meant by consecutive buses
_________________

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rampuria

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Re: PS-Velocity (Must try) [#permalink]

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New post 01 Jun 2009, 02:44
There are lot of assumptions which can be made with Consecutive buses:
1. Oncoming and Overtaking bus
2. Oncoming and the same bus returned back
3. Consecutive buses in same direction

I believe the question is not clear in mentioning the speed of bus and man remains the same.
On assumption we can deal this considering the time asked is for the consecutive buses Overtaking and Oncoming:

Distance between buses = D
Speed of man = Sm
Speed of bus = Sb

Distance = Speed * Time => Time = Distance/Speed = D/Sb

From question:
D/(Sb-Sm) = 12 ---(i)
D/(Sb+Sm)=4 ---(ii)

12(Sb-Sm)=4(Sb+Sm)
=> 3Sb-3Sm=Sb+Sm
=> 2Sb = 4Sm
=> Sb = 2Sm => Sm=Sb/2 ---(iii)
Sub (iii) in (i)
D/(Sb-Sb/2) = 12
D = 12(Sb/2)
=> D= 6Sb => D/Sb = 6
=> Ans: 6 Minutes

Already discussed in bus-and-cycle-72280.html#p534844

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Re: PS-Velocity (Must try)   [#permalink] 01 Jun 2009, 02:44
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