Question 102939: At exactly what time (to the fraction of a minute) between 7:00 and 8:00 do the hands of a clock form a straight angle? Found 2 solutions by MathLover1, ankor@dixie-net.com:Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website! in 1 minute hand has moved 6 degrees (360 degrees/ 60 min)
so
=> to move 180 degrees will need 30 min
180degrees/6degrees/min) = 30 min
Since time range is between 7:00 and 8:00, one hand will be on 7 and other must be on 5 min pass 7 o'clock, or 7:05.
You can put this solution on YOUR website! At exactly what time (to the fraction of a minute) between 7:00 and 8:00 do the hands of a clock form a straight angle?
:
Let x = no. of minutes
:
Convert minutes to degrees, 360/60 = 6 deg/min
:
Convert hours to degrees, 360/12 = 30 deg/hr
:
7 o'clock = 7 * 30 = 210 degrees
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Portion of an hr = (x/60) * 30 = x/2 or .5x
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Hr hand degrees - minute hand degrees = 180
210 + .5x - 6x = 180
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-5.5x = 180 - 210
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-5.5x = -30
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x = -30/-5.5
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x = 5.45 minutes. The time would be 07:05.45 for a straight line of the hands
:
Check our solution
210 + (5.45/60)30 - 5.45(6) =
210 + 2.7 - 32.7 = 180
