Q. 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 scooty with 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.
A) 9 min, 40 km/h
B) 25 min, 100 km/h
C) 10 min, 90 km/h
D) 15 min, 120 km/h
Explanation
[Solution by Claude - not from source] Bus spacing $vT$. Same direction: $vT=(v-60)\times30$; opposite: $vT=(v+60)\times10$ (times in min, speeds per min-consistent). So $3(v-60)=v+60\Rightarrow v=120$ km/h, and $T=\frac{(180)(10)}{120}=15$ min. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.