Question

a backhoe can dig \\(\frac{5}{10}\\) of a ton of dirt in \\(\frac{1}{6}\\) of a hour. compute the unit rate. \
a 1 tons per hour \
b 3 tons per hour \
c 6 tons per hour \
d 9 tons per hour \
e 5 tons per hour

Explanation:

Step1: Recall unit rate formula

Unit rate (tons per hour) is total tons divided by total hours. So we use the formula: Unit Rate = $\frac{\text{Total Tons}}{\text{Total Hours}}$.

Step2: Substitute the given values

We know total tons is $\frac{5}{10}$ and total hours is $\frac{1}{6}$. So substitute into the formula: Unit Rate = $\frac{\frac{5}{10}}{\frac{1}{6}}$.

Step3: Divide the fractions

Dividing by a fraction is multiplying by its reciprocal. So $\frac{\frac{5}{10}}{\frac{1}{6}}=\frac{5}{10}\times6$.

Step4: Simplify the expression

First, simplify $\frac{5}{10}=\frac{1}{2}$. Then $\frac{1}{2}\times6 = 3$.

Answer:

B. 3 tons per hour