IMC 2016 Q24
24. Every day, Aimee goes up an escalator on her journey to work. If she stands still, it takes her 60 seconds to travel from the bottom to the top. One day the escalator was broken so she had to walk up it. This took her 90 seconds.
How many seconds would it take her to travel up the escalator if she walked up at the same speed as before while it was working?
- A 30
- B 32
- C 36
- D 45
- E 75
Intermediate Mathematical Challenge 2016, Question 24. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 36
Let the distance from the bottom of the escalator to the top be \(d\). Then, when she stands still, Aimee travels \(d / 60\) every second. When she is walking, Aimee travels \(d / 90\) every second. So when Aimee walks up the working escalator, the distance which she travels every second is \(\dfrac{d}{60} + \dfrac{d}{90} = \dfrac{3d + 2d}{180} = \dfrac{5d}{180} = \dfrac{d}{36}\). So the required number of seconds is 36.
Solution © UK Mathematics Trust, from the IMC 2016 solutions. Longer versions with investigations: Solutions and investigations (PDF).