Task B-1.4. Ivo and Mate are clearing the road of snow. First, Ivo cleared $\frac{3}{5}$ of the road, and then Mate cleared the remaining part so that the entire road was cleared in 12 hours. How many hours would it take for them to clear the road together if it is known that it would take Mate 5 hours more to clear the road alone than it would take Ivo to clear it alone?
## Solution.

Let $x$ be the number of hours it would take Ivo to clear the road alone.

Then $x+5$ is the number of hours it would take Mate to clear the road alone.

(1 point)

For clearing $\frac{3}{5}$ of the road, Ivo needed $\frac{3 x}{5}$ hours, and for clearing the remaining $\frac{2}{5}$ of the road, Mate needed $\frac{2(x+5)}{5}$ hours.

(1 point)

Since the clearing was completed in 12 hours, we have

$$
\frac{3 x}{5}+\frac{2(x+5)}{5}=12
$$

From this, we get $x=10$,

Ivo can clear the road in 10 hours, and Mate in 15 hours.

(1 point)

Together, they would clear

$$
\frac{1}{10}+\frac{1}{15}=\frac{1}{6} \quad \text{of the road per hour}
$$

They would clear the entire road in 6 hours.