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?

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
RELATED QUESTIONS
The lengths of the hour and minute hands of a clock are 4cm and 6cm respectively. What is (answered by ikleyn)

How many minutes after 5 o�clock, will the minute hand be 16 minute spaces behind the... (answered by ikleyn,Theo)

How many minutes after five o’clock will the hands of the clock be perpendicular for... (answered by Edwin McCravy,greenestamps)

Shortly after 5 O�clock, when the minute hand and the hour hand of the clock made a 90... (answered by richwmiller,greenestamps)

At how many minutes after 3:00 p.m. will the hands of a clock be perpendicular for the... (answered by rfer)

A clock has hour and minute hands 1 and 1.6 inches long respectively. At what rate are... (answered by robertb,ikleyn)

Hello, I don't know how to make and equation out of this. - thanks Your watch loses 1... (answered by Alan3354)

The hour and minute hands of the clock are 4.5 ft and 6.0 ft respectively. How fast are... (answered by Alan3354)

What is the smaller angle in degrees between the hour and minute hands of a clock at... (answered by Alan3354)