GK 2017 Q19
19. Buses leave the airport every 3 minutes to travel to the city centre. A car leaves the airport at the same time as one bus and travels to the city centre by the same route. It takes each bus 60 minutes and the car 35 minutes to travel from the airport to the city centre. How many of these airport buses does the car overtake on its way to the city centre, excluding the bus it left with?
- A 8
- B 9
- C 10
- D 11
- E 13
Grey Kangaroo 2017, Question 19. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 8
Since the car takes 35 minutes to travel from the airport to the city centre and the buses all take 60 minutes, the car will arrive 25 minutes before the bus it left with. Since buses leave the airport every 3 minutes, they will also arrive at the city centre every 3 minutes. Since 25 = 8 × 3 + 1, in the 25 minute spell between the car arriving and the bus it left with arriving eight other buses will arrive. Therefore the car overtook eight airport buses on its way to the city centre.
Solution © UK Mathematics Trust, from the GK 2017 solutions.