Question

Two runners have a race. The first runner decides to run with his full speed v₁=9 m/s over the 250 meters of the race and then slows to v₂=7 m/s for the rest, since he's tired.

The second runner wants to save energy, so he runs with v₃=8 m/s for the whole time.

If the distance of the race is L=500 m, by what time in seconds does the second runner beat the first?

Moral of the story: slightly slower but steadier wins the race.

Answer 1

t₁=250/9 – 250/7 = 63.5 s
t₂ = 500/8 = 62.5 s
Δt=t₁-t₂=63.5 – 62.5 =1 s.

Answer 2

First runner's time =
T1 = 125/9 + 125/7 = 31.75 seconds

Second runner's time =
T2 = 250 m/8 m/s = 31.25 s

T2 - T1 = 0.50 seconds

Answer 3

Elena's answer assumes a 500 m total race length. It is actually half that.