Mathematics: 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

Two passenger train, a and b, 450 km apart, star

noor66

17.01.2022

Let 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

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

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AleciaCassidy

05.08.2020

1 in. = 6 ft.

you would divide 30 by 5, and 66 by 11, and get 6 for both.

best of luck!

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