Question

Two town A and B are connected by a regular bus service with the bus leaving in either direction in t minutes. A Man cycling with a speed of 20 km per hour in the direction a to b notice at a bus goes past him every 20 minutes in the direction of his motion and every 5 minutes in the opposite direction. What is a period of the bus service and what speed do the bus ply on the road?​

Answer 1

Answer:

Two towns A and B are connected by a regulaar bus service with a bus leaving in either direction every T min A man cycling with a speed of 20kmh-1 in the direction A to B notices that a nus goes past him every 18min in the direction of his motion, and every 6min in the opposite direction. ... v=40kmh-1 and T=230h.

Answer 2

Answer:

v =$\frac{100}{3}$ km/h =33.33km/h and T = 2/15 h

Explanation:

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)×(20/60)

From (i), (v - 20)×(20/60) = 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 5 min,

∴ (v + 20)×(5/60) = vT     ...(iii)

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

v =$\frac{100}{3}$ km/h =33.33km/h and T = 2/15 h