document.write( "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? \n" ); document.write( "
Algebra.Com's Answer #707007 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
The hour, minute, and second hands turns around the same center of a watch.
\n" ); document.write( " In how many seconds after 4 o'clock will the hour hand be halfway between the minute and second hands?
\n" ); document.write( ":
\n" ); document.write( "Find the rate of each hand in degrees/sec
\n" ); document.write( "Second hand: 360/60 = 6 degrees/sec
\n" ); document.write( "Minute hand: 360/60*60) = .1 degrees/sec
\n" ); document.write( "Hour hand: 360/(60*60*12) = .008333 degrees/sec
\n" ); document.write( ":
\n" ); document.write( "let t = no. of sec for this to be true
\n" ); document.write( ":
\n" ); document.write( "A 4 o'clock the hour hand is at 120 degrees, the sec and min hands are at 0
\n" ); document.write( "Find the angles in relation to the hour hand
\n" ); document.write( ":
\n" ); document.write( "Second hand angle = minute hand angle
\n" ); document.write( "6t -(120+.008333t) = (120+.00833t) - .1t
\n" ); document.write( "6t - .008333t - 120 = 120 + .008333t - .1t
\n" ); document.write( "5.991667t - 120 = 120 - .091667t
\n" ); document.write( "5.991667t + .091667t = 120 + 120
\n" ); document.write( "6.093334t = 240
\n" ); document.write( "t = 39.45 seconds the hour hand will be halfway between the sec and minutes hands \n" ); document.write( "
\n" );