Clock question

[jbetz]

If a clock loses 1 min 12 secs per hour from 00:00, what will be the time when the clock shows 19:46 that evening?

[Azalian]

20.09 and 43 seconds, I think.

[jbetz]

Wow, I've no idea if you're right or not, my brain cant cope with it. It would be fascinating to see how you worked your answer.

Thanks

[divlong]

The clock is actually registering 58.8 minutes for every hour that passes. So if you divide the shown time in minutes by 58.8 you will get the actual time.

1186/58.8 = 20.17... hours = 20:10:12

[jbetz]

Fantastic, but I don't know how you got 58.8 or how you convert 20.17 to 20:10:17
Sorry if this is too much to ask, but could you possibly break it down a little further?
..or indeed can anyone verify that 20:10:12 is the right answer....(I'll take your word for it divlong)

Thanks for your patience.

[Huderon]

1 minute 12 seconds is 1.2 minutes (12 seconds being one fifth of a minute). The clock only registers 58 minutes and 48 seconds for every hour that passes, hence divlong's 58.8 minutes.

The way I did it is this. The clock loses 6 minutes every 5 hours, so in 15 hours it loses 18 minutes. Add another 4 minutes 48 seconds (to bring the time up to 19:00 hours) and the clock has lost 22 minutes 48 seconds by 19:00.

The clock loses 1.2 seconds per minute, so 46 x 1.2 = 55.2 seconds. Add that to the 22 minutes 48 seconds it has already lost and by 19:46 on the clock it is 23 minutes 43 seconds slow (to the nearest second).

!9:46 + 0:23:43 = 20:09 and 43 seconds as Azalian said originally.

There are other ways to get there - (number of minutes elapsed x loss per minute)/60 will give you the total time lost which you then add on to the time shown on the clock is one, divlong's method is another.

[jbetz]

Brilliant, confirmed then 20:09:43.
Thanks Azalian for providing the correct answer so quickly and thanks to Huderon for taking the time to show how it's worked out.

[divlong]

Huderon's method is OK up to a point but he has got confused between actual time elapsed and time shown on the clock.

When you get to the point where 19 hours has lost 22mins 48seconds that means that the time shown on the clock is 18:37:12. So we actually have to account for an extra 68 minutes and 48 seconds of clock time - not 46 minutes.

That is why our answers differ by a few seconds.

1 minute 12 seconds is 1.2 minutes so the clock is showing 58.8 minutes elapsed for every hour.

So to get the correct time you take displayed time and multiply it by (60 / 58.8)

So, 19 hours and 46 minutes = 1186 minutes.
Divide that by 58.8 to get the actual number of hours elapsed (20.17).
Then, 0.17 hours = 10.2 minutes (0.17 * 60) and 0.2 minutes = 12 seconds.

Hence 20:10:12