IMC 2016 Q5
5. When travelling from London to Edinburgh by train, you pass a sign saying ‘Edinburgh 200 miles’. Then, \(3\frac{1}{2}\) miles later, you pass another sign saying ‘Half way between London and Edinburgh’.
How many miles is it by train from London to Edinburgh?
- A 393
- B \(396\frac{1}{2}\)
- C 400
- D \(403\frac{1}{2}\)
- E 407
Intermediate Mathematical Challenge 2016, Question 5. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 393
By train, the distance in miles of the second sign from Edinburgh is \(200 - 3\frac{1}{2}\). This sign is halfway between London and Edinburgh, so the distance in miles between the two cities is \(2(200 - 3\frac{1}{2}) = 400 - 7 = 393\).
Solution © UK Mathematics Trust, from the IMC 2016 solutions. Longer versions with investigations: Solutions and investigations (PDF).