So someone said to me "If a clock has its little hand just past 8 and the big hand at 8:10, how long before the two hands are in the same position?" I thought it would be a little more than 30.5 minutes since the big hand would move 60 times faster than the little hand. This would have made the time of the holding of the hands 8:40.5

I asked a friend and he took a complex approach. I don't know where he got the 240 degrees from, as I did consider the 360 degrees of a circle as also an approach but the hands would have been 180 degrees apart I would have thought.

He came up with this:

"May,

t=0; x=240 + t

y=60 + 60*t

y moves 60 times faster than x; hence the multiplier; the two values describe intitial locations in degrees when t=0.

x=y, solve for t

Since x=y when both hands are aligned both equations are equivalent.

240 + t = 60 + 60*t

59 * t = 180

t = 180/59 = 3.05

Solve for x = 240 + t = 243.05

Solve for y = 60 + 60 * 3.05 = 243.05 degrees, equivalent to 8:40.50 or 8:40 and 30 seconds."

I don't know how he came up with his answer but it did match mine. He is btw far further knowlegable and educated than I in math and Algebra than I am but he always respects my ways of viewing as well.