SOLUTION: The hour, minute, and second hands turns around the same center of a watch. In how many seconds after 4 o'clock will the hour hand be halfway between the minute and second hands?
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Question 1092285: The hour, minute, and second hands turns around the same center of a watch. In how many seconds after 4 o'clock will the hour hand be halfway between the minute and second hands? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The hour, minute, and second hands turns around the same center of a watch.
In how many seconds after 4 o'clock will the hour hand be halfway between the minute and second hands?
:
Find the rate of each hand in degrees/sec
Second hand: 360/60 = 6 degrees/sec
Minute hand: 360/60*60) = .1 degrees/sec
Hour hand: 360/(60*60*12) = .008333 degrees/sec
:
let t = no. of sec for this to be true
:
A 4 o'clock the hour hand is at 120 degrees, the sec and min hands are at 0
Find the angles in relation to the hour hand
:
Second hand angle = minute hand angle
6t -(120+.008333t) = (120+.00833t) - .1t
6t - .008333t - 120 = 120 + .008333t - .1t
5.991667t - 120 = 120 - .091667t
5.991667t + .091667t = 120 + 120
6.093334t = 240
t = 39.45 seconds the hour hand will be halfway between the sec and minutes hands
