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.

Correct result:

s =  284.7 km

Solution:

$$\begin{gathered} s_1=s_2=s \\ 3.5\cdot v_1=3.05\cdot (v_1+12) \\ {v}_1={\displaystyle \frac{12\cdot 3.05}{3.5-3.05}}=81.33km\mathrm{/}h \\ {v}_2=v_1+12=93.33km\mathrm{/}h \\ s=v_1\cdot 3.5={\displaystyle \frac{3.5\cdot 3.05}{3.5-3.05}}\cdot 12=284.7\text{ km} \end{gathered}$$

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