The distance between two stations is 340 km. Two trains start simultaneously from these stations on parallel tracks to cross each other. The speed of one of them is greater than that of the other by 5 km/hr. If the distance between the two trains after 2 hours of their start is 30 km, find the speed of each train.
Let, the speed of the first train be $x \mathrm{~km} / \mathrm{h}$.
Then, the speed of the other train will be $(\mathrm{x}+5) \mathrm{km} / \mathrm{h}$.
2 hours after they start ed:
Distance of the first train from the starting point $=2 \mathrm{x} \mathrm{km}$
Distance of the other train from the starting point $=2(\mathrm{x}+5) \mathrm{km}$
Now,
$2(\mathrm{x}+5)+2 \mathrm{x}+30=340$
or $4 \mathrm{x}+10+30=340$
or $4 \mathrm{x}=340-40$
or $\mathrm{x}=\frac{300}{4}=75$
$\therefore$ Speed of the first train $=75 \mathrm{~km} / \mathrm{h}$.
Speed of the other train $=(75+5)=80 \mathrm{~km} / \mathrm{h}$.