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# 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 20km/hr in direction A to B notices that a bus goes past him every 18 minutes in the direction of motion and every 6 min in opposite direction. the period T of the bus service is? please answer as soon as possible..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 20km/hr in direction A to B notices that a bus goes past him every 18 minutes in the direction of motion and every 6 min in opposite direction. the period T of the bus service is? please answer as soon as possible..

Arjun Bakshi
37 Points
7 years ago
let speed of bus be  u km/hr.
and the time interval be T min.
distance travelled by cycle in T min =uT
relative velocity of the cycle wrt the bus coming from same side =u-20/60
uT/(u-1/3)=18
uT=18u-6  (1)
relative velocity of cycle wrt to bus coming from diff. side
uT/(u+1/3)=6
uT =6u+2 (2)
Dividing (1) by (2)
6u+2=18u-6
8=12u
u=2/3 km/min
=40 km/h
from(2)
2/3*T=6*2/3 +2
T=9min