Clocks

What distance will describe the tip of a minute hand 6 cm long for 20 minutes when we know the starting position with finally enclosed hands at each other at 120°?

Correct answer:

x =  12.57 cm

Step-by-step explanation:

$$\begin{gathered} r=6\text{cm} \\ o=2\pi \cdot r=2\cdot 3.1416\cdot 6\doteq 37.6991\text{cm} \\ {t}_1=20\text{min} \\ \alpha =120{}^{\circ } \\ {q}_1=\frac{t_1}{60}=\frac{20}{60}=\frac{1}{3}\doteq 0.3333 \\ {q}_2=\frac{\alpha }{360}=\frac{120}{360}=\frac{1}{3}\doteq 0.3333 \\ {q}_1=q_2 \\ x=o\cdot q_1=37.6991\cdot 0.3333=12.57\text{cm} \end{gathered}$$

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