> > Also (to the nearest second):
> > 1: 4.05.27
> > 2: 4.21.49
> > 3: 4.38.11
> > 4: 4.54.33
> >
> > enile ;)
>
> G*D but you're GUD! How do you do it? I suppose you had use of a PC and a math program. But if you remember I only had use of 'improper fractions' back in 1955 in year 5 of high school (don't ask how old I am), I'd appreciate a few notes on how you approach the problem?
>
> Thanks for your time enile ;) you're real sweet!

No PC, no sleight of hand - just good old algebra:

Suppose the time is 4 hours and t minutes
Each 'hour' on the clock face is 30deg
Position of hour hand is: (4 x 30deg) + (t/60 x 30deg) = (120 + t/2)deg
Position of minute hand is: t x 360/60deg = 6t

So, if we want the angle between the hands to be y degrees (where y = -90, 0, 90, 180) we solve the equation:
6t - (120 + t/2) = y
rewritten as t = (120+y)/5.5
remembering that t returned is in decimal minutes, so to convert to minutes and seconds take the bit after the decimal point (the seconds component) and multiply by 60 (eg 1.5 minutes = 1min + 60x0.5sec).

Always glad to help someone with their homework (can't work out how old you are though;)

en'once was a mathematician'ile