Question

Two runners start simultaneously from the same point on a circular 200-m track and run in the same direction. One runs at a constant speed of 6.20 m/s and the other runs at a constant speed of 5.50 m/s.When will the fast one first overtake ("lap") the slower one?How far from the starting point will each have run at that instant?When will the fast one overtake the slower one for the second time?How far from the starting point will they be at that instant?

Answer 1

Answer

given,

length of the track = 200 m

speed of runner 1 = 6.20 m/s

speed of the runner 2 = 5.5 m/s

distance covered by the fastest runner, d = 6.2 t

distance covered by the slow runner,d = 5.50 t + 200

time taken to overtake for the first time

 6.2 t = 5.50 t + 200

  0.7 t = 200

       t = 285.7 s

distance covered from the starting point

 d = 6.2 t

 d = 6.2 x 285.7

 d = 1771.43 m

for next overtaking time taken will be double

 t' = 258.7 x 2 = 571.4 s

distance travel by the runner from the starting point

d' = 6.2 t'

d' = 6.2 x 571.4

d' = 3542.68 m