Magazine, Clock question

[Muzz]

At midnight on Sunday 31st December, Professor Stone sets two of his analogue clocks to the correct time.
One of his clocks gains one minute every hour and the other loses two minutes every hour.

1. When will the clocks next show the same time as each other?
2. When will the clocks both show the correct time?

This is driving me mad! Is there an easy way to work it out? Any help appreciated! Muzz

[sandyRoe]

After the first hour there will be a difference of 3 minutes between the clocks. After 20 hours there will be a difference of one hour. After 240 hours( 10 days) they will show the same time.

[Old_Geezer]

I concur although I worked it slightly differently.

I reckoned they would next show the same time when they were 12 hours difference between them (if you see what I mean).

Every hour they differed by 3 minutes. so 3s into (12*60) = 240 hours.

That said these questions often have a hidden aspect that messes up the obvious answer :-) Or am I just being cynical ?

[sandyRoe]

The clock that is losing one minute each hour will be 4 hours slow when it shows the same time as the other one.
It would take another twenty days until it was showing the correct time.

[Muzz]

Thank you for that! We were trying to do it the long way (i.e. writing it on sheets of paper), and we gave up at Day Nine!! That'll teach us!

I, too, can be cynical, but this is in one of my Mum's magazines, so I thought there HAD to be an answer.

Now working on when they will show the correct time....

Many thanks again!

[Avatar]

after 10 days at midnight. both show 4 o clock
after 20 days " 8 o clock
after 30 days " 12 o clock.

so midnight on 30/31st Jan for correct time?

[Avatar]

Which is what Sandy already said. D'oh!

[Muzz]

Avatar - just back in and thought I'd look at this again! Yes, we got there in the end! I think I'll stick to the general knowledge crosswords - MUCH easier!
Thanks again to all for your help and wisdom, Muzz