Answer
$TW = 27$
$TY = 18$
Work Step by Step
According to the concurrency of medians theorem, the medians of a triangle are concurrent at a point that is two-thirds of the way between each vertex and the midpoint of the side opposite to the vertex.
$\overline{YW}$ is one-third of the way from $T$ to $W$. Let's set up an equation incorporating what we know:
$YW = \frac{1}{3}(TW)$
Let's plug in what we know:
$9 = \frac{1}{3}(TW)$
Divide each side by $\frac{1}{3}$ to solve for $TW$. To divide by $\frac{1}{3}$ means to multiply by its reciprocal, which is $3$:
$TW = 9(3)$
Multiply to solve:
$TW = 27$
If $TW$ is the sum of $YW$ and $TY$, we can subtract $YW$ from $TW$ to get $TY$:
$TY = TW - YW$
Let's plug in what we know:
$TY = 27 - 9$
Subtract to solve:
$TY = 18$
