Clocks

How far does the tip of a clock's minute hand travel in 340 minutes if the minute hand is 23 cm long? How far does the tip of the hour hand travel in the same time?

Final Answer:

m =  818.9 cm
h =  68.2 cm

Step-by-step explanation:

$$\begin{gathered} r=23\text{cm} \\ t=340\text{min} \\ {t}_1=t\to \text{h}=t:60\text{h}=340:60\text{h}=5.66667\text{h} \\ m=2\pi \cdot r\cdot t_1=2\cdot 3.1416\cdot 23\cdot 5.6667=818.9\text{cm} \end{gathered}$$

$$\begin{gathered} t_2=\frac{t}{12\cdot 60}=\frac{340}{12\cdot 60}=\frac{17}{36}\doteq 0.4722 \\ h=2\pi \cdot r\cdot t_2=2\cdot 3.1416\cdot 23\cdot 0.4722=68.2\text{cm} \end{gathered}$$

Try another example