## Task 2 - 010522

During a test flight from Moscow to the Soviet Antarctic observation station Mirny over a total of 25300 km, an aircraft of type "IL 18" covered the last 6700 km in two stages. The first stage was about $1700 \mathrm{~km}$ longer than the second.

How many kilometers did the two stages cover?
Let $a$ be the length of the first stage and $b$ be the length of the second stage. This gives us the equations

$$
a+b=6700 \mathrm{~km} \quad ; \quad a=b+1700 \mathrm{~km}
$$

Substituting the first equation into the second equation yields

$$
(b+1700 \mathrm{~km})+b=6700 \mathrm{~km} \quad \Rightarrow b=2500 \mathrm{~km} \quad ; \quad a=2500 \mathrm{~km}+1700 \mathrm{~km}=4200 \mathrm{~km}
$$

The first stage is $4200 \mathrm{~km}$ and the second stage is $2500 \mathrm{~km}$ long.