Parallel tracks

Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m long and crosses a lamp post in 12 seconds. If the speed of the other train is 6 km/hr less than the faster one, its length, in m, is .........?

Final Answer:

b =  190 m

Step-by-step explanation:

$$\begin{gathered} a=160\text{m} \\ {t}_1=14\text{s} \\ {t}_2=12\text{s} \\ \Delta =6\text{km/h}\to \text{m/s}=6:3.6\text{m/s}=1.66667\text{m/s} \\ {v}_1=a/t_2=160/12=\frac{40}{3}\doteq 13.3333\text{m/s} \\ {v}_2=v_1-\Delta =13.3333-1.6667=\frac{35}{3}\doteq 11.6667\text{m/s} \\ {t}_1=\frac{a+b}{v_1+v_2} \\ b=t_1\cdot (v_1+v_2)-a=14\cdot (13.3333+11.6667)-160=190\text{m} \end{gathered}$$

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