A bus service runs between two cities, with buses departing in either direction at regular interval T. A scooter rider travels at 60 km/h. Buses overtake her every 30 min and approach from the opposite direction every 10 min. Determine T and bus speed.
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Question

A bus service runs between two cities, with buses departing in either direction at regular interval T. A scooter rider travels at 60 km/h. Buses overtake her every 30 min and approach from the opposite direction every 10 min. Determine T and bus speed.

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G1 Physics · Accepted Answer

Step 1: Let bus speed be u km/h. Spacing between consecutive buses in one direction is d = uT (T in hours). Step 2: Same-direction relative speed is u − 60, so d = (u − 60)(30/60) = (u − 60)/2. Step 3: Opposite-direction relative speed is u + 60, so d = (u + 60)(10/60) = (u + 60)/6. Step 4: Equate: (u − 60)/2 = (u + 60)/6 ⇒ 3u − 180 = u + 60 ⇒ u = 120 km/h. Step 5: d = (120 − 60)/2 = 30 km. Service interval T = d/u = 30/120 h = 1/4 h = 15 min. Final answer: T = 15 min, bus speed = 120 km/h, Opt…