Answer
$t=4$ seconds
Work Step by Step
Step 1: The formula to be used here is $s=rwt$.
Step 2: After substituting the values of $s$,$r$ and $w$ provided by the question into this formula, the equation becomes
$\frac{12\pi}{5}=\frac{3}{2}\times \frac{2\pi}{5}\times t$
Step 3: Simplifying, $\frac{12\pi}{5}=\frac{3}{1}\times \frac{\pi}{5}\times t$
Step 4: $\frac{12\pi}{5}=\frac{3\pi}{5}\times t$
Step 5: Multiplying both sides by $\frac{5}{3\pi}$,
$\frac{12\pi}{5}\times\frac{5}{3\pi}=\frac{3\pi}{5}\times t\times\frac{5}{3\pi}$
Step 6: Simplifying, $t=4$ seconds
