Question
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
Ask by Bryant Kelley. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 12\, \frac{1}{2} \) minutes per meter
Solution
To find the unit rate in minutes per meter, follow these steps:
1. **Determine the Given Values:**
- Depth filled: \( \frac{3}{5} \) meters
- Time taken: \( 7 \frac{1}{2} \) minutes (which is \( \frac{15}{2} \) minutes)
2. **Set Up the Proportion:**
We want to find how many minutes it takes to fill 1 meter. Let \( x \) be the number of minutes per meter.
\[
\frac{3}{5} \text{ meters} = \frac{15}{2} \text{ minutes}
\]
\[
1 \text{ meter} = x \text{ minutes}
\]
3. **Solve for \( x \):**
\[
x = \frac{\frac{15}{2} \text{ minutes}}{\frac{3}{5} \text{ meters}} = \frac{15}{2} \times \frac{5}{3} = \frac{75}{6} = \frac{25}{2}
\]
\[
\frac{25}{2} \text{ minutes} = 12 \frac{1}{2} \text{ minutes}
\]
**Answer:**
\( 12\, \frac{1}{2} \) minutes per meter
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Simplify this solution Extra Insights
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.
