Obviously, from 6 o'clock to 7 o'clock sharp, the hour hand and the minute hand can make an angle of 1 10 degrees twice.

Set the door at 6 o'clock X.

If it doesn't exceed 6: 30,

180 degrees-(x/60) * 360+(360/12) * (x/60) =110 degrees.

The solution x= 140/ 1 1 is about equal to 12.7 points.

If it's past 6: 30,

[(x-30)/60] * 360-(360/12) * (x/60) =1/0 degrees.

The solution x=580/ 1 1 is about 52.7 points.

So the departure time is 6: 00, 12: 42, and the return time is 6: 52: 42. It takes 52.7- 12.7=40 (minutes) to do business.