Relative Motion

Question 1

Men are running along a road at 15 km/h behind one another at equal intervals of 20m.Cyclists riding in the same direction at 25 km/h at equal intervals of 30 m. At what speed in km/hr an observer travel along the road in opposite direction so that whenever he meets a runner he also meets a cyclist
Speed of Runner = 15 km/hr = 15 * 1000/3600 = 25/6 m/s
Speed of cyclist = 25 km/hr = 25 * 1000/3600 = 125/18 m/s
Distance Covered by Observer = x m
Then Distance Covered by Runner & Cyclist = 20 x & 30  x
Time taken by cyclist & Runner is same
( 20 x)/(25/6) = ( 30 x)/(125/18)
=> 5 (20x) = 3 (30 x)
=> 100  5x = 90  3x
=> 2x = 10
=> x = 5
Time taken by runner = (20  5)/(25/6) = 90/25 = 18/5 = 3.6 sec
Speed of Observer = 5 / (18/5) = 25/18 m/s
= (25/18) * 3600/1000 km/hr
= 5 km/Hr

@yashkapoor
Thanks