IMC 2010 Q16
16. Albert Einstein is experimenting with two unusual clocks which both have 24-hour displays. One clock goes at twice the normal speed. The other clock goes backwards, but at the normal speed. Both clocks show the correct time at 13:00.
What is the correct time when the displays on the clocks next agree?
- A 05:00
- B 09:00
- C 13:00
- D 17:00
- E 21:00
Intermediate Mathematical Challenge 2010, Question 16. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 21:00
After \(x\) hours, the first clock will have gone forward \(2x\) hours and the second clock will have gone back \(x\) hours. So the next time they agree is when \(2x + x = 24\), that is when \(x = 8\). The correct time then is 21:00.
Solution © UK Mathematics Trust, from the IMC 2010 solutions.