Two trains

Two trains departed from City A and City B against each other. They met after some time. The first train took 9 hours to reach city B, and the second took 4 hours to reach city A. In what proportion were the train speeds?

Correct answer:

r =  2:3

Step-by-step explanation:

$$\begin{gathered} r=v_1:v_2 \\ s=s_1+s_2 \\ {s}_1=v_1\cdot t \\ {s}_2=v_2\cdot t \\ {s}_2=9v_1 \\ {s}_1=4v_2 \\ 4v_2=v_{1}t \\ 9v_1=v_{2}t \\ \frac{9v_1}{4v_2}=\frac{v_2}{v_1} \\ \frac{9v_1^2}{4v_2^2}=1 \\ \frac{v_1^2}{v_2^2}=\frac{4}{9} \\ \frac{v_1}{v_2}{}^2=\frac{4}{9} \\ \frac{v_1}{v_2}=\sqrt{\frac{4}{9}}=\frac{2}{3} \\ r=\frac{v_1}{v_2} \\ r=2:3=\frac{2}{3}\approx 0.6667 \end{gathered}$$

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