Question

a mine extracts \\(\frac{5}{7}\\) tons of iron from \\(\frac{3}{4}\\) hours of work. what is the extraction rate per hour?

Explanation:

Step1: Recall rate formula

Rate = Amount / Time, so extraction rate = iron extracted / time taken.

Step2: Substitute values

Iron extracted = $\frac{5}{7}$ tons, time = $\frac{3}{4}$ hours. So rate = $\frac{5}{7} \div \frac{3}{4}$.

Step3: Divide fractions

Dividing by a fraction is multiplying by its reciprocal: $\frac{5}{7} \times \frac{4}{3} = \frac{20}{21}$.

Answer:

$\frac{20}{21}$ tons per hour