Let V be the speed of the bus running between towns A and B.
Speed of the cyclist = 20 km/hr
Relative speed of bus moving in the direction of the cyclist = V - v = (V-20) km/hr
Every 18 mins, the bus went past the cyclist. moving in the direction of the bus.
Distance covered by the bus =
One bus leaves every t minutes.
Distance travelled by the bus = V ... (ii)
Equations (i) and (ii) are equal.
Relative speed of the bus moving in the opposite direction of the cyclist = (V + 20) km/h
Time taken by the bus to go past the cyclist = 6 min = 6 / 60 h
Now, from equations (3) and (4), we get