#### Answer

$\frac{19}{3}t$

#### Work Step by Step

"The quotient of" tells us that we need to divide the number 19 by the number 3, which we can represent as the fraction $\frac{19}{3}$. "The product of $t$ and the quotient of 19 and 3" tells us that we need to multiply $t$ by this quotient, giving us $\frac{19}{3}t$.