Every 1 min, the minute hand angle is 6 degrees, and the hour hand angle is 0.5 degrees.

(1) Suppose the departure time is 6: 00, and x: 0.5x+(180-6x) =110.

Solvable: x=70/5.5

(2) Assuming that the time to go home is 6: 00, the equation can be listed as:180-(360-6y)-0.5y =110.

Solvable: y=290/5.5

So the time to go out is: y-x = (290-70)/5.5=220/5.5=40 (minutes).