1. **State the problem:** We need to find the length in hours of two workout plans, Plan A and Plan B, given the number of clients and total training hours on Monday and Tuesday. 2. **Define variables:** Let $x$ be the length in hours of Plan A, and $y$ be the length in hours of Plan B. 3. **Write the system of equations:** - Monday: $9x + 7y = 12$ - Tuesday: $3x + 5y = 6$ 4. **Solve the system using substitution or elimination.** We'll use elimination: Multiply the second equation by 3 to align coefficients of $x$: $$3(3x + 5y) = 3(6) \Rightarrow 9x + 15y = 18$$ 5. **Subtract the first equation from this new equation:** $$ (9x + 15y) - (9x + 7y) = 18 - 12 \Rightarrow 8y = 6 $$ 6. **Solve for $y$:** $$ y = \frac{6}{8} = \frac{3}{4} = 0.75 $$ 7. **Substitute $y=0.75$ into the first equation:** $$ 9x + 7(0.75) = 12 \Rightarrow 9x + 5.25 = 12 $$ 8. **Solve for $x$:** $$ 9x = 12 - 5.25 = 6.75 \Rightarrow x = \frac{6.75}{9} = 0.75 $$ 9. **Interpretation:** Each Plan A workout lasts $0.75$ hours (45 minutes), and each Plan B workout also lasts $0.75$ hours (45 minutes). **Final answer:** - Length of Plan A workout: $0.75$ hour(s) - Length of Plan B workout: $0.75$ hour(s)