The minute hand goes six degrees per minute and the hour hand goes half a degree per minute. Suppose it's exactly six o'clock, and the minute hand and the hour hand differ by one hundred and eighty degrees.

Suppose that after six o'clock, the minute hand is separated from the hour hand by 1 10 degrees, so it takes x minutes to rotate from six o'clock sharp.

2/ 1x+ 180-6x = 1 10

X= 140/ 1 1 (minutes)

When it is close to seven o'clock, the minute hand is 1 10 degrees away from the hour hand. Then it takes x minutes to turn from six o'clock sharp.

6x- 180-2/ 1x = 1 10

X=580/ 1 1 (minutes)

580/11-140/1= 440/1= 40 (minutes)

It takes Xiaoming's father 40 minutes to go out.