13. Luca began a $520 \mathrm{~km}$ trip by car with 14 litres of fuel in the car tank. His car consumes 1 litre of fuel per $10 \mathrm{~km}$. After driving $55 \mathrm{~km}$, he saw a road sign showing the distances from that point to five petrol stations ahead on the road. These distances are $35 \mathrm{~km}, 45$ $\mathrm{km}, 55 \mathrm{~km}, 75 \mathrm{~km}$ and $95 \mathrm{~km}$. The capacity of the car's fuel tank is 40 litres and Luca wants to stop just once to fill the tank.
How far is the petrol station that he should stop at?
A $35 \mathrm{~km}$
B $45 \mathrm{~km}$
C $55 \mathrm{~km}$
D $75 \mathrm{~km}$
E $95 \mathrm{~km}$
Solution
D

Luca starts with 14 litres of fuel, which is enough for $140 \mathrm{~km}$. After travelling $55 \mathrm{~km}$, Luca can go a further $85 \mathrm{~km}$. Hence, he cannot reach the $95 \mathrm{~km}$ petrol station, but can reach the others. If he stops at the $55 \mathrm{~km}$ petrol station (or any nearer one), then he will have at least $410 \mathrm{~km}$ left to travel of his $520 \mathrm{~km}$ journey, but his tank only holds enough for $400 \mathrm{~km}$. Hence, he should stop at the $75 \mathrm{~km}$ petrol station, with $390 \mathrm{~km}$ left to travel.