A passenger

A passenger train, 150 m long, passes a railway platform, 200 m long, in 35 seconds.
Find:
1) speed of the train in km/h
2) the time taken by the train to pass a man cycling in the direction of the train at the rate of 9 km/h.

Correct answer:

v =  36 km/h
t₂ =  20 s

Step-by-step explanation:

$$\begin{gathered} a=150\text{m} \\ b=200\text{m} \\ t=35\text{s} \\ {v}_1=\frac{a+b}{t}=\frac{150+200}{35}=10\text{m/s} \\ v=v_1\to \text{km/h}=v_1\cdot 3.6\text{km/h}=10\cdot 3.6\text{km/h}=36\text{km/h}=36\text{km/h} \end{gathered}$$

$$\begin{gathered} v_2=9\text{km/h}\to \text{m/s}=9:3.6\text{m/s}=2.5\text{m/s} \\ {t}_2\cdot v_1=a+t_2\cdot v_2 \\ {t}_2\cdot 10=150+t_2\cdot 2.5 \\ 7.5t_2=150 \\ {t}_2=\frac{150}{7.5}=20 \\ {t}_2=20=20\text{s} \end{gathered}$$

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