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) = -(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) = -(16)/(7)v+450\end{cases}\implies 2v = -(16)/(7)v+450`

Solving this equation for v we have

`2v = -(16)/(7)v+450 \iff (30)/(7)v=450 \iff v=(450\cdot 7)/(30) = 105`

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

`105\cdot (8)/(7) = 15\cdot 8=120 \text{ km/h}`