A girl leaves her home in the morning for school. She looks for the time on an old-fashioned, analog clock, through a mirror. Unfortunately there are no digits on the clock, so she mistakes the mirror image for the actual time. She rides her bike to school, which takes twenty minutes. When she arrives and looks at the school clock, it shows a time two-and-a-half hours later than the mirror image she saw at home.
What was the time when she left home? What was the mirror image? And when did she arrive?
Note: There can be different answers, depending on whether she sees the length difference of the two clock arms (hour and minute) or not. There is at least one answer if she can see the length difference, and another answer if she can’t.
Answer
If she can’t see the length difference, the following works fine:
When she looks at the clock it is 12.10, and she sees 10.00. So, after twenty minutes of travelling the time is 12.30, which is 2.5 hours later than 10.00.
If she can see the length difference, the following works:
When see looks at the clock it is 19.05, and she sees 16.55. Twenty minutes later the tame is 19.25, which is 2.5 hours later than 16.55.
This also works if she can’t see the length difference.