Clocks

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

Correct answer:

x =  12.57 cm

Step-by-step explanation:

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

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