Expert: Richard J. Raridon - 5/19/2010

Question
1)  At what time between 2 and 3 o'clock are the hands of the clock be 15 minutes apart?

2)  At what time after between 7 and 8 o'clock are the hands of a clock be 20 minutes apart?

3) Find two different times between 11 and 12 o'clock when the hands of a clock are at right angles to each other?

If you can, you can use this:
x = the number of minute spaces moved by the minute hand
x/12 = the number of minute spaces moved by the hour hand
or if you want your own way to solve this, you can!

Thanks :)

Answer
1) What you really mean is "when are the hands at right angles to each other?"
no. of degrees per minute for the minute hand = 6
no. of degrees per minute for the hour hand = 0.5
net no. of degrees per minute = 5.5
The hour hand starts at 60 degrees so 60+0.5m+90 = 6m so m = 27.3 minutes or 2:27.3
2) At 7PM the hands are 210 degrees apart so 210+0.5m-6m = 120 so m = 16.36m past 7.  
3) The hour hand starts at -30 degrees so 30-0.5m +6m = 90 and m = 10.9 minutes or 11:10.9
Later, 330 +0.5m -6m = 90 so m = 43.6 minutes or 11:43.6