Δt₁ = 6 с, Δt₂ = 8 с, v₃ = 1,5*v₁
1-й забег
t₁ = S / v₁ - Вася
t₂ = S / v₂ - Петя
t₁ - t₂ = Δt₁ => S / v₁ - S / v₂ = Δt₁
S*(v₂ - v₁) / (v₁*v₂) = Δt₁ - (1)
2-й забег
t₃ = S / v₃ = S / (1,5*v₁)
t₂ - t₃ = Δt₂
S / v₂ - S / (1,5*v₁) = Δt₂
S*(1,5*v₁ - v₂) / (1,5*v₁*v₂) = Δt₂ - (2)
первое делим на второе
(v₂ - v₁)*1,5 / (1,5*v₁ - v₂) = Δt₁ / Δt₂
Δt₁ / Δt₂ = k = 6 с / 8 с = 3/4 = 0,75
1,5*(v₂ - v₁) = (1,5*v₁ - v₂)*k
1,5*v₂ - 1,5*v₁ = 1,5*k*v₁ - k*v₂
1,5*v₂ + k*v₂ = 1,5*k*v₁ + 1,5*v₁
v₂*(1,5 + k) = 1,5*v₁*(k + 1)
v₂ / v₁ = 1,5*(k + 1) / (1,5 + k)
v₂ / v₁ = 1,5 * (0,75 + 1) / (1,5 + 0,75) = 1,5 * 1,75 / 2,25 = 7/6 ≈ 1,2
