IMC 2011 Q20
20. Max and his dog Molly set out for a walk. Max walked up the road and then back down again, completing a six mile round trip. Molly, being an old dog, walked at half Max's speed. When Max reached the end of the road, he turned around and walked back to the starting point, at his original speed. Part way back he met Molly, who then turned around and followed Max home, still maintaining her original speed. How far did Molly walk?
- A 1 mile
- B 2 miles
- C 3 miles
- D 4 miles
- E 5 miles
Intermediate Mathematical Challenge 2011, Question 20. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 4 miles
Let Max and Molly meet after the latter has travelled \(x\) miles. Then Max has travelled \((6 - x)\) miles. So \(6 - x = 2x\), thus \(x = 2\). Therefore Molly walks a total of 4 miles.
Solution © UK Mathematics Trust, from the IMC 2011 solutions. Longer versions with investigations: Solutions and investigations (PDF).