Question

23) In a 5000 m race, the athletes run 1212 laps; each lap is 400 m. Kara runs the race at a constant pace and finishes in 17.9 min. Hannah runs the race in a blistering 15.3 min, so fast that she actually passes Kara during the race.

How many laps has Hannah run when she passes Kara?​

Answer 1

D = distance traveled to complete the race = 5000 m

t_k = time taken by kara to complete the race = 17.9 min = 17.9 x 60 = 1074 sec

Speed of kara is given as

v_k = D/t_k    Eq-1

t_h = time taken by hannah to complete the race = 15.3 min = 15.3 x 60 = 918 sec

Speed of hannah is given as

v_h = D/t_h                                                                    Eq-2

Using Eq-1 and Eq-2, relative speed is given as

v = v_h - v_k = (D/t_h ) - (D/t_k)

t = time

Using the equation for one lap as

v t = 400

((D/t_h ) - (D/t_k)) t = 400

((5000/918) - (5000/1074)) t = 400

t = 505.61 sec

distance traveled by hannah is given as

d = v_h t

d = (5000/918) (505.61)

d = 2753.87 m

number of laps are given as

n = d/400

n = 2753.87/400

n = 6.88