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…

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 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. 1. 9 min, 40 km/h 2. 25 min, 100 km/h 3. 10 min, 90 km/h 4. 15 min, 120 km/h

Doubtly AI · Accepted Answer

Answer: 4. 15 min, 120 km/h Key idea: buses in one direction are spaced vT apart. The girl meets them at the rate set by the relative speed. Let bus speed be v km/h, girl's speed 60 km/h. Same direction: the gap is covered at relative speed v-60 in 30 min; opposite direction: relative speed v+60 in 10 min. spacing=vT=(v-60)×30=(v+60)×10\ \ (same time unit) 30v-1800=10v+600⇒ v=120\ km/h Spacing =(v+60)×10/60=180×1/6=30 km, so T=30/120\ mathrm h=15 min.

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…

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