Let V be the speed of the bus running between towns A and B.
Speed of the cyclist, v = 20 km/h
Relative speed of the bus moving in the direction of the cyclist
= V – v = (V – 20) km/h
The bus went past the cyclist every (18/60)h min i.e., (when he moves in the direction of the bus)
Distance covered by the bus = (V - 20) (18/60)km .......................(i)
Since one bus leaves after every T minutes, the distance travelled by the bus will be equal to:
V x T/60 .............................(ii)
Both equations (i) and (ii) are equal.
(V - 20) x 18/60 = VT/60.................................(iii)
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 = 6min = (6/60)h
Substituting the value of V in equation (iv), we get
(40+20) x 6/60 = 40T/60
T= 360/40 = 9min