SOLUTION: What is the first time after 4 o'clock that the hands of the clock make an angle of 65degree?

Question 64841: What is the first time after 4 o'clock that the hands of the clock make an angle of 65degree?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
What is the first time after 4 o'clock that the hands of the clock make an angle of 65 degrees?
:
We know:
minute hand travels 360/60 = 6 deg/min
hour hand travels 360/(60*12) = .5 deg/min
:
Starting out at 4 o'clock: min hand at 0 degrees, hr hand at 120 degrees
:
Let m = number of minute when hands are 65 degrees apart
:
hr hand - min hand = 65
(120 + .5m) - 6m = 65
.5m - 6m = 65 - 120
-5.5m = -55
m = -55/-5.5
m = 10 minutes
We can say then, that at 4:10 the hands will be 65 deg apart:
;
Check our solution using hand position
hr hand in 10 min from 120 degrees = 120 + (10*.5) = 125 deg
min hand in 10 min from 0 degrees = 10*6 = 60 deg
125 - 60 = 65 degree
:
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