Clock Angle Rate of Change

At 8:48 am:

• Position of minute hand $= 48 \times 6^\circ = 288^\circ$
• Position of hour hand $= 8 \times 30^\circ + 48 \times 0.5^\circ = 240^\circ + 24^\circ = 264^\circ$
• Minor angle between them $= 288^\circ - 264^\circ = 24^\circ$.

An increase of 50% means the new angle becomes $24^\circ \times 1.5 = 36^\circ$. So the angle needs to increase by $12^\circ$.

Relative speed of minute hand with respect to hour hand $= 6^\circ - 0.5^\circ = 5.5^\circ = \frac{11}{2}^\circ$ per minute.

Time required $= \frac{12}{11/2} = \frac{24}{11}$ minutes.