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Two town A and B are connected by a regu...

Two town A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man leaving in either direction every in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. The period T of the bus service is

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Let speed of each bus `=v hm h^(-1)`
The distance between the nearest buses plying on either car
`=vT km` (i)
For buses going grom town `A` to `B`:
Relative speed of bus in this direction go past the cyclist after every `18 min`. Theteftore, separation between the buses
`=(v-20)xx(18)/(60)`
From (i), `(v-20)xx(18)/(60)=vT` (ii)
For buses coming from `B` to `A` :
The relative velocity of bus respect to man`=(v+20)`
`becuase (v+20)xx(6)/(60)=vT` ...(iii)
Solving (ii) and (iii), we get
`v=40 km h^(-1)` and `T=(2)/(30)h`.
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