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6.12
s = 24 km
t₁ - czas faktyczny biegu [h]
t₂ - czas przy zwiększonej prędkości [h]
t₂ = t₁ - 1
Δv = 4 km/h
v śr = ?
v = s/t
v₁ = s/t = 24/t₁
v₂ = s/t₂ = s/(t₁ -1) = 24/(t₁ -1)
v₁ + 4 = v₂
24/t₁ + 4 = 24/(t₁ -1) |t₁(t₁ -1)
24(t₁ -1) + 4t₁(t₁ -1) = 24t₁
24t₁ - 24 + 4t₁² - 4t₁ = 24t₁
4t₁² - 4t₁ - 24 = 0
4(t₁² - t₁ - 6) = 0 /:4
t₁² - t₁ - 6 = o
Δ = 1 + 24 = 25
√Δ = 5
t₁ > 0
t₁ = (1+5)/2
t₁ = 3 [h]
v sr = 24km/3h
v śr = 8 km/h