#### Answer

$4\pi$ inches

#### Work Step by Step

Step 1: The formula to be used here is $s=r\theta$ where $s$ is the length of the arc intercepted on a circle of radius $r$ by a central angle of measure $\theta$ radians.
Step 2: In this case, $r=3$ inches.
Step 3:
$60$ minutes= $2\pi$ radians
$40$ minutes= $x$ radians
Using ratios and cross multiplication:
$\frac{60}{2\pi}=\frac{40}{x}$
$60x=80\pi$
$x=\frac{80\pi}{60}=\frac{4\pi}{3}$
Therefore, $40$ minutes represents $\frac{4\pi}{3}$ radians.
Step 4: The distance traveled by the tip of the minute hand is represented by the arc length $s$.
Step 5: Therefore $s=r\theta=(3)(\frac{4\pi}{3})=4\pi$ inches