Men are running along a road at 15 km/h behind one another at equal intervals of 20 m. Cyclists are riding in the same direction at 25 km/h at equal intervals of 30 m. At what speed (in km/h) an observer travel along the road in opposite direction so that whenever he meets a runner he also meets a cyclist? (neglect the size of cycle)
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(5 )
Sol. Let u = speed of observer.
Relative velocity between observer and a man .
= u + 15 km/h.
Relative velocity between observer and a cyclist.
= u + 25 km/h.
Hence , to for a man and a cyclist to meet simultaneously
= 
⇒ u = 5 km/h
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