Question

At what time between 3 O'Clock and 4 O'Clock will the two hands coincide ?

Answer 1

In a minute, the hour hand moves by half degrees and the minute hand moves by six degrees.
The angle at 3 o'clock between the two hands is 90 degrees.
For them to coincide, it should move m minutes
$90=0+(6m-\frac{m}{2})$

$180=12mm$

$180=11m$

$m=16\frac{4}{11}$

It should be $16\frac{4}{11}$ past 3 for the two hands to coincide.