**Question:**

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.

**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.