Find the earliest time after 3 PM that the hour hand and minute hand of a clock overlap. Give your answer with an exact number of minutes.
0=abs((30*3) - (5.5*M)), solve for M
M =180 / 11 =16.36363636.....etc. =16 minutes and about 22 seconds after 3 PM
+128407 Let tthe top of the clock = 0°
At 3 PM the minute hand will be at this position
And the hour hand will be at 90°
The minute hand moves at 6° per minute
The hour hand moves at .5° per minute
So when they overlap the distance they are from the top of the clock will be the same..so....using rate * tme = distance we have that
6T = 90 + (.5)T subtract .5T from both sides
5.5 T = 90 divide both sides by 55
T ≈ 16.36 min after 3 PM
