Answer
$t=\dfrac{50xy}{r}$
Work Step by Step
$t$ is directly proportional to $xy$ and inversely proportional to $r$ so the equation that relates the variables is:
$t=k \cdot \frac{xy}{r}$ where k = constant of proportionality.
If x = 2, y = 3, and r = 12, then t = 25. Substitute these values into the equation above to have:
$t=k \cdot \frac{xy}{r}
\\25 = k \cdot \frac{2(3)}{12}
\\25=\frac{6k}{12}
\\25=\frac{k}{2}
\\25(2)=k
\\50=k$
The constant of proportionality is $50$. Thus, the equation that relates t, x, y, and r is:
$t=50 \cdot \frac{xy}{r}
\\t=\frac{50xy}{r}$
