Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T min. A man cycling with a speed of 20 ~km / h from A to B notices that a bus travelling in the direction of his motion goes past him every 18 ~min and every 6 ~min he notices a bus travelling in the opposite direction go past him. Assuming that, the buses travel with a constant speed. Find T and the constant speed

Step-by-step solution

Let, the speed of bus be v_B and that of cyclist be v_C . Case 1 Bus moving from A to B , Relative speed of bus =v_B-v_C=v_B-20 Distance covered = Velocity Time d= (v_B-20 ) 18...(i) Case 2 Bus moving from B to A , Relative speed of bus =v_B+v_C =v_B+20 Distance covered = Velocity Time d= (v_B+20 ) 6...(ii) From Eqs. (i) and (ii), we get aligned & (v_B-20 ) 18= (v_B+20 ) 6 & v_B=40 ~km / h & From Eq. (ii), (v_B+20 ) 6=v_B T & (40+20) 6=40 T & T=9 = 9 60 ~h = 3 20 ~h . & aligned