The speed of the hour hand is v1 = 2 Pi / (24*60) radii / min

The speed of the minute hand is v2 = 2 Pi / 60 radii / min

let p be the line between the middle of the clock and the number 3

After 1 hour and x minutes the angle between:

- the hour hand and the p line will be x*v1

- the minute hand and the p line will be pi/2 - x*v2

and they are equal

x*v1 = pi/2 - x*v1

x*2 Pi / (24*60) = pi/2 - x*2 Pi / 60 divide both sides by pi

x/720 = 1/2 - x/30

x = 14.4 min

The solution is 1 hour and 14.4 min = 74.4 minutes.