Question

Two towns a and b are connected 2 points
by a regular bus service with a bus
leaving in either direction every T
minutes. A man cycling with a speed
of 20 km per hour in the direction a
to b notices that a bus goes past him
every 18 minute in the direction of his
motion, and every 6 minut in the
opposite direction. What is the
period t of the bus service and with
what speed do the buses ply on the
road​

Answer 1

Let the speed of each bus = v km/h

The distance between the nearest buses plying on either car = vT km...(i)

For buses going from town A to B:

Relative speed of bus in the direction of motion of man = (v - 20)

Buses plying in this direction go past the cyclist after every 18 min. Therefore, separation between the buses

= (v - 20)×(18/60)

From (i), (v - 20)×(18/60) = vT ...(ii)

For buses coming from B to A:

The relative velocity of bus with respect to man = (v + 20) Buses coming from town B past'the cyclist after every 6 min,

∴ (v + 20)×(6/60) = vT ...(iii)

Solving (ii) and (iii), we get\

v = 40 km/h and T = 2/30 h

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