Chapter 6 - Rational Expressions and Equations - 6.7 Applications Using Rational Equations and Proportions - 6.7 Exercise Set - Page 430: 76

40

We know that at the end of the time, the hot tub needs to be full. Thus, letting $t$ be the time it takes to fill, we find: $$ 1=\frac{1}{8}t-\frac{1}{10}t\\ \frac{1}{8}t\cdot \:40-\frac{1}{10}t\cdot \:40=1\cdot \:40\\ 5t-4t=40 \\ t=40$$