Question

Train A departs from Point A with a velocity of 150 km/h, Train B departs from Point B with a velocity of 100 km/h, and the distance between point A and B is 500 km. How long will it take for the trains to meet?

Answer 1

Let us consider the initial position of train A, $s_{0A}=0$. This implies that $s_{0B}=500$.

Moreover, we have

$v_A=150, \quad v_B=-100$

This implies that the two equations are

$s_A(t)=150t,\quad s_B(t)=500-100t$

The two trains meet if and only if their positions are the same, at the same time:

$s_A(t)=s_B(t) \iff 150t=500-100t \iff 250t=500 \iff t=2$

So, the two trains meet after 2 hours.

Answer 2

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