Question

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

Explanation:

Step1: Convert mixed number to improper fraction

$8\frac{3}{4} = \frac{35}{4}$

Step2: Calculate rate per hour

$\text{Rate} = \frac{35}{4} \div \frac{5}{6} = \frac{35}{4} \times \frac{6}{5} = \frac{210}{20} = \frac{21}{2} = 10.5$ (Note: $\frac{21}{2}$ is the simplified fraction, which is 10.5 as a decimal, but the exact fractional answer is $\frac{21}{2}$? Wait correction: Wait 35 divided by 5 is 7, 6 divided by 4 is 3/2, so 7*3/2=21/2. Yes, correct.)
Wait wait no: 8 3/4 is 8 + 3/4 = 35/4? Wait 84=32 +3=35 yes. Then 35/4 divided by 5/6 is 35/4 6/5 = (356)/(45) = (7*6)/4 = 42/4 = 21/2. Yes, that's right. So the exact answer is 21/2 or 10.5, but as a fraction it's 21/2.

Wait wait I think I made a typo earlier, corrected now:

Step1: Convert mixed number to improper fraction

$8\frac{3}{4} = \frac{35}{4}$

Step2: Compute rate per hour

$\frac{35}{4} \div \frac{5}{6} = \frac{35}{4} \times \frac{6}{5} = \frac{21}{2}$

Answer:

$\frac{51}{2}$