## Subject 2.

Let x denote the additional length of road that the first team works on each day compared to the previous day.

Team 1 builds: $1 \mathrm{~km}$ on the first day, $(1+\mathrm{x}) \mathrm{km}$ on the second day, $(1+2 \mathrm{x}) \mathrm{km}$ on the third day, ..., $(1+59 \mathrm{x}) \mathrm{km}$ on the 60th day $\Rightarrow 1+59 x=3 \Rightarrow x=\frac{2}{59} \mathrm{~km}$

The length of the road built by the first team is:

$$
1+1+\frac{2}{59}+1+2 \cdot \frac{2}{59}+\cdots+1+59 \cdot \frac{2}{59}=60+\frac{2}{59}(1+2+\cdots+59)
$$

$=60+\frac{2}{59} \cdot 59 \cdot 60: 2=120 \mathrm{~km}$ 3 p.

Let y denote the length of road that the second team works on less each day compared to the previous day.

Team 2 builds: $4 \mathrm{~km}$ on the first day, $(4-\mathrm{x}) \mathrm{km}$ on the second day, $(4-2 \mathrm{x}) \mathrm{km}$ on the third day, $(4-59 x) \mathrm{km}$ on the 60th day. $\Rightarrow 4-59 x=1 \Rightarrow x=\frac{3}{59} \mathrm{~km}$

The length of the road built by the second team is:

$$
4+4-\frac{3}{59}+4-2 \cdot \frac{3}{59}+\cdots+4-59 \cdot \frac{3}{59}=4 \cdot 60-\frac{3}{59}(1+2+\cdots+59)
$$

$=4 \cdot 60-\frac{3}{59} \cdot 59 \cdot 60: 2=150 \mathrm{~km}$
## Subject 2.

The highway between towns A and B was built by two teams of workers in 60 days. The first team starts from A and completes $1 \mathrm{~km}$ on the first day, then increases the distance by the same length each subsequent day, until the last day when they complete $3 \mathrm{~km}$. The second team starts from $\mathrm{B}$, completes $4 \mathrm{~km}$ on the first day, then decreases the distance by the same length each subsequent day, until the last day when they complete $1 \mathrm{~km}$. What is the length of the highway?