Question

Two trains simultaneously left points $M$ and $N$ and headed towards each other.

The distance between point $M$ and point $N$ is $380$ mi.

The speed of the train, which started, from point $N$ was $5$mph faster than the speed of the other train.

In two hours after the departure the distance between the trains was $30$ mi.

What is the speed of each train?

Answer 1

Use the formula of speed and time to calculate the speed of the train:

Let the speed of the train $M$ be $x$, then the speed of the train $N$ will be $x+5$.

Now, the distance between points $M$ and $N$ is $380$ miles and at the time of $2$ hours, the distance between the trains was $30$ mi.

Since, $Distance=speed\times time$

For the train $M$ distance was $D=x\times 2$ and for the train $N$ distance was $D=\left(5+x\right)\times 2$

Therefore, the distance between the points $M$ and $N$ is,

$$\begin{gathered} 2x+2(x+5)+30=380 \\ \Rightarrow 2x+2x+10+30=380 \\ \Rightarrow 4x+40=380 \\ \Rightarrow 4x=340 \\ \Rightarrow x=85\mathrm{mph} \end{gathered}$$

Thus, the speed of the train $N$ is $85+5=90$ mph.

Hence, the speed of train $MandN$ will be $85$ mph and $90$ mph.