Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving a scooty with a speed of 60 km h⁻¹ in the direction X to Y, and notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in t…

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 is driving a scooty with a speed of 60 km h⁻¹ in the direction X to Y, and 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.

Accepted Answer

(2) 15 min, 120 km h⁻¹. Given: buses every T min each way at speed v; scooty at 60 km h⁻¹ from X to Y; overtaking gap 30 min, oncoming gap 10 min. Idea: consecutive buses are always a fixed distance vT apart, and the girl closes that gap at the relative speed. Buses in her direction: (v-60)×30=vT. Buses in the opposite direction: (v+60)×10=vT. Equating: 30v-1800=10v+600, so 20v=2400 and v=120 km h⁻¹. Then vT=(120-60)×30=1800, so T=(1800)/(120)=15 min.

Step-by-step solution

Why the other options are wrong