Train

Find the average speed of a train (in km/h) that passes a telegraph pole in 7 seconds and passes a 378 m platform in 25 seconds. How long is the train?

Correct answer:

v =  75.6 km/h
l =  147 m

Step-by-step explanation:

$$\begin{gathered} t_1=7\text{s} \\ {t}_2=25\text{s} \\ n=378\text{m} \\ v=s/t \\ {v}_1\cdot t_1=l \\ {v}_1\cdot t_2=l+n \\ {v}_1\cdot 7=l \\ {v}_1\cdot 25=l+378 \\ l-7v_1=0 \\ l-25v_1=-378 \\ Row2-Row1\to Row2 \\ l-7v_1=0 \\ -18v_1=-378 \\ {v}_1=\frac{-378}{-18}=21 \\ l=0+7v_1=0+7\cdot 21=147 \\ l=147 \\ {v}_1=21 \\ v=v_1\to \text{km/h}=v_1\cdot 3.6\text{km/h}=21\cdot 3.6\text{km/h}=75.6\text{km/h} \\ \text{ Verifying Solution: } \\ {T}_1=l/v_1=147/21=7\text{s} \\ {T}_2=(l+n)/v_1=(147+378)/21=25\text{s} \end{gathered}$$

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