4. Matkov's father goes to work by car. On Monday, he drove to work at a speed of 60 km/h and arrived one minute late. On Tuesday, he left at the same time, on the same route, but drove at a speed of 65 km/h and arrived one minute early. What is the length of the route that Matkov's father travels from home to work and back each day?
4. Let $s x$ denote the length of the path from home to work in kilometers.

1 point

When Matko's father drives at a speed of $65 \mathrm{~km} / \mathrm{h}$, he arrives 1 minute earlier,

and when he drives at a speed of $60 \mathrm{~km} / \mathrm{h}$, he arrives 1 minute later.

The difference is 2 minutes or $\frac{2}{60}=\frac{1}{30}$ hours.

2 points

The time spent on the road at a speed of $65 \mathrm{~km} / \mathrm{h}$ is $\frac{x}{65}$ hours,

and the time spent on the road at a speed of $60 \mathrm{~km} / \mathrm{h}$ is $\frac{x}{60}$ hours.

We can write:

$\frac{x}{60}-\frac{x}{65}=\frac{1}{30}$.

4 points

Then we have $65 x-60 x=130$, $5 x=130$,

$x=26 \mathrm{~km}$.

2 points

Matko's father travels a distance of $52 \mathrm{~km}$ each day from home to work and back. 1 point TOTAL 10 POINTS