Men run along a road at 15 km h⁻¹, spaced 20 m apart. Cyclists ride in the same direction at 25 km h⁻¹, spaced 30 m apart. An observer moves in the opposite direction so that whenever he meets a runner he also meets a cyclist. Find the observer's speed in km h⁻¹.
Physics · Kinematics part-3 Relative motion · Relative motion in one dimension
JEE Mains NEET

Question

Men run along a road at 15 km h⁻¹, spaced 20 m apart. Cyclists ride in the same direction at 25 km h⁻¹, spaced 30 m apart. An observer moves in the opposite direction so that whenever he meets a runner he also meets a cyclist. Find the observer's speed in km h⁻¹.

Physics · Kinematics part-3 Relative motion · Relative motion in one dimension

G1 Physics · Accepted Answer

Let observer speed in the opposite direction be u. Time between successive meetings with runners: tₘ = 20/(u+15). Time between successive meetings with cyclists: t꜀ = 30/(u+25). For simultaneous meetings: 20/(u+15) = 30/(u+25). 20u+500 = 30u+450 u=5 km h⁻¹.