PK 2020 Q13
13. Luca began a 520 km trip by car with 14 litres of fuel in the car tank. His car consumes 1 litre of fuel per 10 km. After driving 55 km, he saw a road sign showing the distances from that point to five petrol stations ahead on the road. These distances are 35 km, 45 km, 55 km, 75 km and 95 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 km
- B 45 km
- C 55 km
- D 75 km
- E 95 km
Pink Kangaroo 2020, Question 13. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 75 km
Luca starts with 14 litres of fuel, which is enough for 140 km. After travelling 55 km, Luca can go a further 85 km. Hence, he cannot reach the 95 km petrol station, but can reach the others. If he stops at the 55 km petrol station (or any nearer one), then he will have at least 410 km left to travel of his 520 km journey, but his tank only holds enough for 400 km. Hence, he should stop at the 75 km petrol station, with 390 km left to travel.
Solution © UK Mathematics Trust, from the PK 2020 solutions.