19. (6 points) At a little past six in the evening, Zhang Qiang went out to exercise, at which time the angle between the hour and minute hands was $110^{\circ}$; when he returned home, it was not yet seven, and the angle between the hour and minute hands was still $110^{\circ}$. Therefore, Zhang Qiang spent $\qquad$ minutes exercising.
【Solution】Solution: According to the problem, we know:
The minute hand initially lags the hour hand by $\frac{110}{6}$ spaces;
Later, the minute hand leads by $\frac{110}{6}$ spaces, so the distance difference is $\frac{110}{6} \times 2=\frac{110}{3}$ spaces.
The time spent exercising is: $\frac{110}{3} \div\left(1-\frac{1}{12}\right)=40$ (minutes);
Therefore, the answer is: 40.