Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl driving a scooty at a speed of 60 km/h in the direction X to Y notices that a bus g

Question

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl driving a scooty at a speed of 60 km/h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.

Vishal Gupta · Accepted Answer

D. Let bus speed be v. Same direction: buses catch her every 30 min, so \frac{vT}{v - 60} = 30; opposite: \frac{vT}{v + 60} = 10. Dividing, \frac{v + 60}{v - 60} = 3 \Rightarrow v = 120 km/h, then T = \frac{30 	imes 60}{120} = 15 min.

Motion in a Straight Line