[MOVED] Can you tell time? (time when hands overlap)

[pianoplaya16]

At exactly what time between 1 o' clock and 2 o' clock is the minute hand exactly over the hour hand?

 

[skeeter]

simple ... just solve this equation for "t", which will be the number of minutes after 1:00

\(\displaystyle \L \frac{t}{5} = 1 + \frac{t}{60}\)

 

[TchrWill]

At exactly what time between 1 o' clock and 2 o' clock is the minute hand exactly over the hour hand?

Alternatively:

The angle between each digit on the clock face is 30º.

The hour hnd moves at the rate of 5º/min.

The minute hand moves at the rate of 6º/min.

Therefore, the number of minutes, t, after 1 o'clock fot hands to overlap is given by

.....6t = 30 + .5t or 5.5t = 30 making t = 5.5454 minutes or 5m-27.27sec after 1 0'clock

 

[Denis]

In 12 hours, there are 11 times when the hands are exactly one above the other.

12 / 11 = 1 hour, 5 minutes and 27 3/11 seconds

Next will be twice above, or 2:10:54 6/11