darcy harvests $8\\frac{3}{4}$ acres of corn every $\\frac{5}{6}$ of an hour. darcy harvests corn at a…

darcy harvests $8\\frac{3}{4}$ acres of corn every $\\frac{5}{6}$ of an hour. darcy harvests corn at a constant rate. how many acres does she harvest per hour? enter an exact answer, without rounding. \\boxed{} acres per hour

darcy harvests $8\\frac{3}{4}$ acres of corn every $\\frac{5}{6}$ of an hour. darcy harvests corn at a constant rate. how many acres does she harvest per hour? enter an exact answer, without rounding. \\boxed{} acres per hour

Answer

}=\frac{a\times c + b}{c}). So, (8\frac{3}{4}=\frac{8\times4 + 3}{4}=\frac{32+3}{4}=\frac{35}{4}) acres.

Step2: Find the rate per hour

Rate is equal to the amount of work done divided by the time taken. Here, the amount of work (area harvested) is (\frac{35}{4}) acres and the time is (\frac{5}{6}) hours. To find the rate per hour, we divide the area by the time: (\frac{35}{4}\div\frac{5}{6}). When dividing fractions, we multiply by the reciprocal, so (\frac{35}{4}\times\frac{6}{5}).

Step3: Simplify the multiplication

First, we can cancel out common factors. 35 and 5 have a common factor of 5: (35\div5 = 7) and (5\div5 = 1). 6 and 4 have a common factor of 2: (6\div2 = 3) and (4\div2 = 2). So now we have (\frac{7}{2}\times\frac{3}{1}=\frac{21}{2}). Converting this back to a mixed number (though the problem asks for an exact answer, it can also be written as a mixed number or improper fraction; here (\frac{21}{2}=10\frac{1}{2})).

Answer:

(\frac{21}{2}) (or (10\frac{1}{2}))