PK 2019 Q13
13. The triathlon consists of swimming, cycling and running. The cycling accounts for three-quarters of the total distance, the running for one-fifth and the swimming for 2 km. What is the total distance of this triathlon?
- A 10 km
- B 20 km
- C 38 km
- D 40 km
- E 60 km
Pink Kangaroo 2019, Question 13. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 40 km
The cycling and running account for \(\tfrac{3}{4} + \tfrac{1}{5} = \tfrac{15}{20} + \tfrac{4}{20} = \tfrac{19}{20}\) of the distance. So the swimming, which is 2 km, is the remaining \(\tfrac{1}{20}\) of the distance. Hence the distance is 20 × 2 = 40km.
Solution © UK Mathematics Trust, from the PK 2019 solutions.