IMC 2010 Q18
18. Supergran walks from her chalet to the top of the mountain. She knows that if she walks at a speed of 6 mph she will arrive at 1 pm, whereas if she leaves at the same time and walks at 10 mph, she will arrive at 11 am.
At what speed should she walk if she wants to arrive at 12 noon?
- A 7.5 mph
- B \(7\frac{1}{7}\) mph
- C 7.75 mph
- D \(\sqrt{60}\) mph
- E 8 mph
Intermediate Mathematical Challenge 2010, Question 18. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 7.5 mph
Let the distance from the chalet to the top of the mountain be \(x\) miles. Then, at 6 mph Supergran would take \(\dfrac{x}{6}\) hours, whereas at 10 mph she would take \(\dfrac{x}{10}\) hours. So \(\dfrac{x}{6} - \dfrac{x}{10} = 2\), that is \(5x - 3x = 60\), so \(x = 30\). Hence Supergran's departure time is 8 am and to arrive at 12 noon she should walk at \(\dfrac{30}{4}\) mph, that is \(7\tfrac{1}{2}\) mph.
Solution © UK Mathematics Trust, from the IMC 2010 solutions.