5. A truck and a bus started towards each other simultaneously from two entrances to the highway. Assume that the truck maintains a constant average speed and covers $27 \mathrm{~km}$ in 18 minutes. Assume that the bus also maintains its own constant average speed, which allows it to cover $864 \mathrm{~m}$ in 28.8 seconds. If they met at a common rest area after 2 hours and 45 minutes of such driving, how far apart were their two starting entrances to the highway?

## Tasks worth 10 points:
First solution.

One hour has 60 minutes, so 2 hours and 45 minutes $=120+45=165$ minutes.

The truck travels $27 \mathrm{~km}$ in 18 minutes, which means it travels $27: 18=1.5 \mathrm{~km}$ in 1 minute. $\quad 1$ POINT

In 165 minutes, the truck travels $165 \cdot 1.5=247.5 \mathrm{~km}$.

$1 \mathrm{POINT}$

$1 \mathrm{~km}=1000 \mathrm{~m}$, so $864 \mathrm{~m}=0.864 \mathrm{~km}$,

1 minute $=60$ seconds, so 28.8 seconds $=28.8: 60=0.48$ minutes.

$1 \mathrm{POINT}$

The bus travels $0.864 \mathrm{~km}$ in 0.48 minutes, which means it travels $0.864: 0.48=1.8 \mathrm{~km}$ in 1 minute.

1 POINT

In 165 minutes, the bus travels $165 \cdot 1.8=297 \mathrm{~km}$. 1 POINT

The total distance traveled by the truck and the bus, or the sum of these distances, is the distance between the two entrances to the highway, $247.5+297=544.5 \mathrm{~km}$.

$1 \mathrm{POINT}$

TOTAL 6 POINTS

##