3. A passenger train traveling from Osijek to Zagreb covers $5 \mathrm{~km}$ every 3 minutes. Another passenger train traveling from Split to Zagreb covers $3 \mathrm{~km}$ every 2 minutes. The length of the route from Osijek to Zagreb is 275 km, and the length of the route from Split to Zagreb is $405 \mathrm{~km}$. At what hours must the train from Split depart, and at what hour must the one from Osijek depart if both need to be in Zagreb by $17 \mathrm{~h}$, and we know that the train from Split (due to poor weather conditions) will be delayed by one minute every 30 minutes?
3. A passenger train traveling from Osijek to Zagreb covers $5 \mathrm{~km}$ every 3 minutes. Another passenger train traveling from Split to Zagreb covers $3 \mathrm{~km}$ every 2 minutes. The length of the route from Osijek to Zagreb is 275 km, and the length of the route from Split to Zagreb is 405 km. At what time must the train from Split depart, and at what time must the one from Osijek depart if both need to arrive in Zagreb at $17 \mathrm{~h}$, and we know that the train from Split (due to poor weather conditions) will be delayed by one minute every 30 minutes?

## Solution.

If the passenger train from Osijek to Zagreb covers $5 \mathrm{~km}$ every 3 minutes, then for the entire journey it needs: $275: 5 \cdot 3=55 \cdot 3=165 \mathrm{~min}$.

Since $1 \mathrm{~h}=60 \mathrm{~min}$, the journey from Osijek to Zagreb takes $2 \mathrm{~h}$ and $45 \mathrm{~min}$.

$1 \mathrm{POINT}$

If the passenger train from Split to Zagreb covers $3 \mathrm{~km}$ every 2 minutes, then for the entire journey it needs:

$405: 3 \cdot 2=135 \cdot 2=270 \mathrm{~min}$.

2 POINTS

Since $1 \mathrm{~h}=60 \mathrm{~min}$, the journey from Split to Zagreb takes $4 \mathrm{~h}$ and $30 \mathrm{~min}$.

$1 \mathrm{POINT}$

Since the train from Split is delayed by 1 minute every 30 minutes, it will be delayed in total by:

$4 \cdot 2+1=8+1=9 \mathrm{~min}$.

$1 \mathrm{POINT}$

The total travel time of the train from Split to Zagreb is 4 h and 39 min.

$1 \mathrm{POINT}$

For the train from Osijek to arrive in Zagreb at 17 h (and it travels for 2 h and $45 \mathrm{~min}$), it must depart from Osijek

at 14 h and 15 min.

$1 \mathrm{POINT}$

For the train from Split to arrive in Zagreb at 17 h (and it travels for 4 h and 39 min), it must depart from Split

at 12 h and 21 min.

1 POINT

TOTAL 10 POINTS