The distance between two stations is 300 km.
The distance between two stations is 300 km. Two motorcyclists start simultaneously from these stations and move towards each other. The speed of one of them is 7 km/h more than that of the other. If the distance between them after 2 hours of their start is 34 km, find the speed of each motorcyclist. Check your solution.
Let the speed of one motorcyclist be $x \mathrm{~km} / \mathrm{h}$.
So, the speed of the other motorcyclist will be $(x+7) \mathrm{km} / \mathrm{h}$.
Distance travelled by the first motorcyclist in 2 hours $=2 x \mathrm{~km}$
Distance travelled by the second motorcyclist in 2 hours $=2(x+7) \mathrm{km}$
Therefore,
$300-(2 x+(2 x+14))=34$
$\Rightarrow 300-(2 x+2 x+14)=34$
$\Rightarrow 300-4 x-14=34$
$\Rightarrow 286-4 x=34$
$\Rightarrow 286-34=4 x$
$\Rightarrow 252=4 x$
$\Rightarrow x=\frac{252}{4}=63$
Therefore, the speed of the first motorcyclist is $63 \mathrm{~km} / \mathrm{h}$.
The speed of the second motorcyclist is $(\mathrm{x}+7)=(63+7)=70 \mathrm{~km} / \mathrm{h}$.
Check:
The distance covered by the first motorcyclist in 2 hours $=63 \times 2=126 \mathrm{~km}$
The distance covered by the second motorcyclist in 2 hours $=70 \times 2=140 \mathrm{~km}$
The distance between the motorcyclists after 2 hours $=300-(126+140)=34 \mathrm{~km}$ (which is the same as given)
Therefore, the speeds of the motorcyclists are $63 \mathrm{~km} / \mathrm{h}$ and $70 \mathrm{~km} / \mathrm{h}$, respectively.