In the hour that begins at the time shown, for how long is the angle between the hands LESS than 60°?

At 7:00 the minute hand is 210° behind and gains 5.5° a minute. The angle is under 60° while the gap is between 150° and 270°: from 150 ÷ 5.5 = 27 3/11 min to 270 ÷ 5.5 = 49 1/11 min. That lasts 49 1/11 − 27 3/11 = 21 9/11 min. (27 3/11 min is when the window opens; 20 min treats the gain as 6° a minute.)