The given information is the dollars Julia earns varies directly as the number of hours she works.
Also, d=$116.25 when t=15 h.
The formula for the direct variation is:
[tex]d=k\cdot t[/tex]Where k is the constant of variation.
Replace the known values and find k:
[tex]\begin{gathered} 116.25=k\cdot15 \\ k=\frac{116.25}{15} \\ k=7.75 \end{gathered}[/tex]Now, to find t when d=178.25, replace d and k and solve for t in the direct variation equation:
[tex]\begin{gathered} 178.25=7.75\cdot t \\ t=\frac{178.25}{7.75}^{} \\ t=23\text{ hours} \end{gathered}[/tex]The answer is t=23 hours
