As I traveled up and down our great glorious country, I found myself in a place where the tempature goes up sharply in the day and down at night. This had an effect on my watch, I noticed it was 1/2 a minute faster at nightfall, but at dawn it had lost 1/3 minute, making it only 1/6 minute fast.
One morning- May 1- my watch showed the right time. By what date was it 5 minutes faster?
In 24 hours the watch gained 1/2-1/3= 1/6 minute. It would seem it would be 5 minutes fast in 5 X 6= 30 days; that is,the morning of May 31. But already on the morning of May 28 the was 27/6= 4 1/2 minutes fast. At the close of the day the watch gained 1/2 minute more, so it was 5 minutes fast on may 28.