Question
A construction company can remove \( 7 \frac{1}{2} \) metric tons of dirt from a construction site in \( 3 \frac{1}{8} \) hours. What is the unit rate in metric tons per hour? Write your answer as a fraction or a mixed number in simplest form.
Ask by Burns Murray. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The unit rate is \( 2 \frac{2}{5} \) metric tons per hour.
Solution
To find the unit rate in metric tons per hour, we need to divide the total amount of dirt removed by the total time taken.
Given:
- **Total dirt removed**: \( 7 \frac{1}{2} \) metric tons
- **Total time taken**: \( 3 \frac{1}{8} \) hours
**Step 1: Convert mixed numbers to improper fractions.**
\[
7 \frac{1}{2} = \frac{15}{2}
\]
\[
3 \frac{1}{8} = \frac{25}{8}
\]
**Step 2: Divide the two fractions.**
\[
\text{Unit rate} = \frac{\frac{15}{2}}{\frac{25}{8}} = \frac{15}{2} \times \frac{8}{25} = \frac{120}{50}
\]
**Step 3: Simplify the fraction.**
\[
\frac{120}{50} = \frac{12}{5} = 2 \frac{2}{5}
\]
**Final Answer:**
\[
2 \frac{2}{5}\ \text{metric tons per hour}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find the unit rate in metric tons per hour, we need to divide the total amount of dirt removed by the total time taken. First, convert both mixed numbers to improper fractions. For \( 7 \frac{1}{2} \): \[ 7 \frac{1}{2} = \frac{15}{2} \] For \( 3 \frac{1}{8} \): \[ 3 \frac{1}{8} = \frac{25}{8} \] Now, we divide the amount of dirt by the time: \[ \text{Unit rate} = \frac{\frac{15}{2}}{\frac{25}{8}} = \frac{15}{2} \times \frac{8}{25} = \frac{15 \times 8}{2 \times 25} = \frac{120}{50} = \frac{12}{5} \] Thus, the unit rate is \( \frac{12}{5} \) metric tons per hour, which can also be expressed as \( 2 \frac{2}{5} \) metric tons per hour in mixed number form.
