To find out how many acres Darcy harvests per hour, divide the total acres she harvests by the fraction of an hour she spends harvesting.
Darcy harvests \(8\dfrac{3}{4}\) acres every \(\dfrac{5}{6}\) of an hour.
First, convert the mixed number \(8\dfrac{3}{4}\) to an improper fraction. \(8\dfrac{3}{4}\) is the same as \(8 \times 4 + 3\) all over \(4\), which equals \(35/4\).
Now, to find out how many acres she can harvest in one hour (which is what "per hour" means), you perform the following division operation:
\[
\text{acres per hour} = \frac{\text{acres}}{\text{fraction of an hour}} = \frac{35/4}{5/6}.
\]
To divide by a fraction, you multiply by its reciprocal. The reciprocal of \(\dfrac{5}{6}\) is \(\dfrac{6}{5}\).
So you multiply \(35/4\) by \(6/5\):
\[
\frac{35}{4} \times \frac{6}{5} = \frac{35 \times 6}{4 \times 5}.
\]
Now do the multiplication:
\[
\frac{35 \times 6}{4 \times 5} = \frac{210}{20}.
\]
Now simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which in this case is 10:
\[
\frac{210}{20} = \frac{210 \div 10}{20 \div 10} = \frac{21}{2}.
\]
So Darcy harvests \(\dfrac{21}{2}\) or 10.5 acres per hour.
Darcy harvests
\[8\dfrac{3}4\] acres of corn every
\[\dfrac{5}6\] of an hour. Darcy harvests corn at a constant rate.
How many acres does she harvest per hour?
1 answer