Chapter 10 - Exponents and Radicals - 10.6 Solving Radical Equations - 10.6 Exercise Set - Page 669: 70

$$t=230$$

We first solve for $t$: $$1087.7\sqrt{\frac{9t+2617}{2457}}=S\\ \left(\sqrt{\frac{9t+2617}{2457}}\right)^2=\left(\frac{S\cdot \:10}{10877}\right)^2\\ t=\frac{245700S^2-309614990593}{1064782161}$$ Plugging in the given value of $S$: $$t=\frac{245700\left(1502.3\right)^2-309614990593}{1064782161} \\ t=230$$