Question

Two passenger train, A and B, 450 km apart, star to move toward each other at the same time and meet after 2hours.
If train B, travels 8/7 as fast as train A. Find the speed of each train

Answer 1

Let $v$ be the speed of train A, and let's set the origin in the initial position of train A. The equations of motion are

$\begin{cases}s_A(t) = vt\\s_B(t) = -\dfrac{8}{7}vt+450\end{cases}$

where $s_A,\ s_B$ are the positions of trains A and B respectively, and t is the time in hours.

The two trains meet if and only if $s_A=s_B$, and we know that this happens after two hours, i.e. at $t=2$

$\begin{cases}s_A(2) = 2v\\s_B(2) = -\dfrac{16}{7}v+450\end{cases}\implies 2v = -\dfrac{16}{7}v+450$

Solving this equation for v we have

$2v = -\dfrac{16}{7}v+450 \iff \dfrac{30}{7}v=450 \iff v=\dfrac{450\cdot 7}{30} = 105$

So, train A is travelling at 105 km/h. This implies that train B travels at

$105\cdot \dfrac{8}{7} = 15\cdot 8=120 \text{ km/h}$