Question

The minute hand of a clock is exactly 6in in length, and the tip of the minute hand has traveled ten inches since noon. What time is it?

Answer 1

$\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}\qquad \begin{cases} r=radius\\ \theta =angle\ in\\ \qquad degrees\\ ------\\ r=6\\ s=10 \end{cases}\implies 10=\cfrac{\theta \pi 6}{180}\implies \cfrac{180\cdot 10}{6\pi }=\theta \\\\\\ \cfrac{300}{\pi }=\theta \implies 95.49^o\approx \theta$

now, the circle of the clock has 360°, if we divide it by 60(minutes), we get 360/60, just 6° for each minute.

now, if there are 6° in 1 minute, how many minutes in 95.49°?

well, just 95.49/6 or about 15.92 minutes, I take it you can round it up to 16 minutes.

so 16 minutes since noon, so is about 12:16, about time get the silverware for lunch.