Ahmad fills an aquarium to a depth of \( \frac{3}{5} \) meters in \( 7 \frac{1}{2} \) minutes. What is the unit rate in minutes per meter? Write your answer as a fraction or a mixed number in simplest form minutes

To find the unit rate in minutes per meter, first, convert \( 7 \frac{1}{2} \) minutes to an improper fraction: \( 7 \frac{1}{2} = \frac{15}{2} \) minutes. Now, since the aquarium is filled to a depth of \( \frac{3}{5} \) meters, we can set up the ratio: \[ \text{Unit rate} = \frac{\text{Total time}}{\text{Depth}} = \frac{\frac{15}{2} \text{ minutes}}{\frac{3}{5} \text{ meters}} \] To divide by a fraction, multiply by its reciprocal: \[ \text{Unit rate} = \frac{15}{2} \times \frac{5}{3} = \frac{15 \times 5}{2 \times 3} = \frac{75}{6} = \frac{25}{2} \] Thus, the unit rate is \( \frac{25}{2} \) minutes per meter, which can also be expressed as \( 12\frac{1}{2} \) minutes per meter.