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.

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.