SOLUTION: At what time between 7pm and 8pm will the minute hand be 90 degrees behind the hour hand?
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Question 567470: At what time between 7pm and 8pm will the minute hand be 90 degrees behind the hour hand?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Each hour mark on the clock is of
a degree circle apart. That is degrees
At 7 pm, the minute hand and hour hand are
degrees apart
The minute hand is moving at the rate of degrees/min
The hour hand is moving at the rate of degree/min
------------------
Let = the degrees that the minute hand travels until it makes
an angle of degrees with the hour hand
Let = the degrees that the hour hand travels until it makes
an angle of degrees with the minute hand
Let = time in minutes until they are degrees apart
------------------
(1)
(2)
(3)
------------------
This is 3 equations and 3 unknowns, so it's solvable
Substitute (2) and (3) into (1)
(1)
(1)
(1)
(1)
(1) min
sec
The hands will be 90 degrees apart at 21 min and 49 sec past 7 PM
hope I got it
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