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.

t₁=250/9 – 250/7 = 63.5 s

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

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

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

To determine the time it takes for each runner to complete the race, we can use the formula:

Time = Distance / Speed

Let's calculate the time for each runner:

For the first runner:
Time₁ = (250 m) / (9 m/s) + (250 m) / (7 m/s)
Time₁ = 27.78 s + 35.71 s
Time₁ ≈ 63.49 s

For the second runner:
Time₂ = (500 m) / (8 m/s)
Time₂ = 62.5 s

To determine by how much the second runner beats the first runner, we subtract the time of the first runner from the time of the second runner:

Time difference = Time₂ - Time₁
Time difference = 62.5 s - 63.49 s
Time difference ≈ -0.99 s

The negative value indicates that the first runner actually finishes the race slightly faster than the second runner. Therefore, the moral of the story "slightly slower but steadier wins the race" does not apply in this scenario.