6. Mia finished \( 60 \% \) of her homework in 45 minutes. How many minutes will it take her to complete all of her homework at this rate?

To find out how many minutes it will take Mia to complete all of her homework at the rate she is currently working, we can use the concept of proportionality. Let's denote the total time it will take Mia to complete all of her homework as \( t \) minutes. Since Mia has already finished \( 60\% \) of her homework in 45 minutes, we can set up a proportion to find the total time: \[ \frac{60\%}{45\, \text{minutes}} = \frac{100\%}{t\, \text{minutes}} \] Now, we can solve for \( t \) to find the total time it will take Mia to complete all of her homework. Solve the equation by following steps: - step0: Solve for \(t\): \(\frac{60\%}{45}=\frac{100\%}{t}\) - step1: Find the domain: \(\frac{60\%}{45}=\frac{100\%}{t},t\neq 0\) - step2: Divide the terms: \(\frac{1}{75}=\frac{1}{t}\) - step3: Swap the sides: \(\frac{1}{t}=\frac{1}{75}\) - step4: Rewrite the expression: \(t=75\) - step5: Check if the solution is in the defined range: \(t=75,t\neq 0\) - step6: Find the intersection: \(t=75\)