Two persons

Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. Find the length of the train.

Correct answer:

x =  500 m

Step-by-step explanation:

$$\begin{gathered} v_1=2\text{km/h}\to \text{m/s}=2:3.6\text{m/s}=0.55556\text{m/s} \\ {v}_2=4\text{km/h}\to \text{m/s}=4:3.6\text{m/s}=1.11111\text{m/s} \\ {t}_1=90\text{s} \\ {t}_2=100\text{s} \\ {v}_1<v_2 \\ x=(v-v_1)\cdot t_1 \\ x=(v-v_2)\cdot t_2 \\ (v-v_1)\cdot t_1=(v-v_2)\cdot t_2 \\ (v-0.55555555555556)\cdot 90=(v-1.1111111111111)\cdot 100 \\ 10v=61.111111 \\ v=\frac{61.11111111}{10}=6.11111111 \\ v=\frac{55}{9}\doteq 6.111111 \\ x=(v-v_1)\cdot t_1=(6.1111-0.5556)\cdot 90=500\text{m} \end{gathered}$$

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