I came across a question in an ICAS exercise booklet for primary school in Australia. Ihe question is as follows:
At midnight on Friday, Megan's clock showed the correct time as 0:00 am.
At midnight on Saturday, her clock showed the time as 11:48 pm.
At midnight on Sunday, her clock showed the time as 11:36 pm.
At 6.00 am on Monday, Megan set her clock so that it showed 6:02 am.
What is the time difference, in minutes, between Megan's clock and the correct time of midnight on Thrusday the same week?
I calcuated the result as 43 minutes, but the key says it is 45 minutes. I'm not sure whether I've done it wrong or the key isn't right, or both. Please help me solve this problem. Thank you very much in advance.
You are correct.
Assuming that the clock loses $12$ minutes in $24$ hours, from $6\text{ am}$ on Monday to $12\text{ midnight}$ on Thursday, the clock would have lagged by $\frac{12}{24}(18+24\times3)-2=43$ minutes, considering that Megan set it $2$ minutes ahead initially.
Edit: As pointed out in the comments by Doug M, If you count the end of Wednesday as Thursday's midnight (i.e. day begins at 00:00 hrs), you would have $24$ less hours in the sum above, giving a lag of $43-12=31$ minutes.