# Trains

On double track line between stations K and M went against each other two trains. The first train passed the distance between stations for 3.5 hours, the second, which had an average speed of 12 km/h more passed for 3.05 hours.

Calculate the distance between stations K and M.

Result

s =  284.7 km

#### Solution:

$s_1 = s_2 = s \ \\ 3.5 \cdot v_1 = 3.05 \cdot (v_1 + 12) \ \\ v_1 = \dfrac{ 12 \cdot 3.05 }{ 3.5 - 3.05 } = 81.33 \ km/h \ \\ v_2 = v_1 + 12 = 93.33 \ km/h \ \\ \ \\ s = v_1 \cdot 3.5 = \dfrac{ 3.5 \cdot 3.05 }{ 3.5 - 3.05 } \cdot 12 = 284.7 \ \text{km}$

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