Question 689727
 start at 12 o'clock: when will the minute hand catch the hour hand? (this was a problem given to me 60 yrs ago--am I right in remembering the answer to be 16 4/11?)
:
I don't think so, won't the minute hand catch up with the hour hand after one hr?
The hour hand will be slightly passed 1 when the minute hand catches it.
:
Using degrees, one hr = 30 degrees, 1 min = 6 degrees
:
let m = minutes after the hr when this happens
:
Hour hand degrees = min hand degrees
30 + {{{m/60}}}*30 = 6m
30 + {{{m/2}}} = 6m
mult by 2
60 + m = 12m
60 = 12m - m
60 = 11m
m = 60/11
m = 5{{{5/11}}} minutes when it catches the hour hand