Question

A track athlete runs the 1,600 m race, which is 4 laps around a 400 m track. She runs the first 3 laps at an average speed of 3.8 m/s, and the last lap at an average speed of 5.1 m/s. What is her average speed for the entire race?

A 4.70 m/s

B 2.23 m/s

C 4.06 m/s

D 4.45 m/s

E 8.90 m/s

Answer 1

Length of each lap = L = 400 m

Average speed of the athlete for the first 3 laps = V₁ = 3.8 m/s

Time taken by the athlete to complete the first 3 laps = T₁

V₁T₁ = 3L

(3.8)T₁ = 3(400)

T₁ = 315.79 sec

Average speed of the athlete for the last lap = V₂ = 5.1 m/s

Time taken by the athlete to complete the last lap T₂

V₂T₂ = L

(5.1)T₂ = 400

T₂ = 78.43 sec

Total time taken by the athlete to complete the 4 laps = T

T = T₁ + T₂

T = 315.79 + 78.43

T = 394.22 sec

Average speed of the athlete for the entire race = V

VT = 4L

V(394.22) = 4(400)

V = 4.06 m/s

Average speed of the athlete for the entire race = 4.06 m/s