# A train leaves a station and travels north at a speed of 45 ​km/h. Two hours​ later, a second train leaves on a parallel track and travels n

Question

A train leaves a station and travels north at a speed of 45 ​km/h. Two hours​ later, a second train leaves on a parallel track and travels north at 75 ​km/h. How far from the station will they​ meet?

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1 year 2021-08-31T01:11:29+00:00 1 Answers 5 views 0

The trains will meet 225km north from the station.

Explanation:

First, we need the equation of position of the two trains. Since they have constant velocities, these equations are:

$$x_1=v_1(t+t_0)\\\\x_2=v_2t}$$

Where $$t_0$$ is the time the first train is traveling before the second train levaes the station. When the trains meet, $$x_1=x_2=x$$ . If we solve for t in the equations above, we have:

$$t=\frac{x}{v_1}-t_0\\ \\t=\frac{x}{v_2}$$

Matching these equations and solving for x, we obtain:

$$\frac{x}{v_1}-t_0=\frac{x}{v_2}\\\\xv_2-v_1v_2t_0=xv_1\\\\x(v_2-v_1)=v_1v_2t_0\\\\x=\frac{v_1v_2t_0}{v_2-v_1}\\ \\\implies x=\frac{(45km/h)(75km/h)(2h)}{75km/h-45km/h}=225km$$

In words, the trains will meet 225km north from the station.