Darcy harvests 8(3)/(4) acres of corn every (5)/(6) of an hour. Darcy harvests corn at a constant rate. How many acres does she harvest per hour? acres per hour

Question

Darcy harvests  8(3)/(4) acres of corn every  (5)/(6) of an hour. Darcy harvests corn at a constant rate. How many acres does she harvest per hour? acres per hour

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. Darcy harvests 8(3/4) acres of corn every 5/6 of an hour. We need to find out how many acres she harvests in one full hour.Convert to improper fraction: Convert the mixed number to an improper fraction. 8(3/4) is the same as 8 + 3/4. To convert it to an improper fraction, multiply the whole number 8 by the denominator 4 and add the numerator 3. 8 * 4 = 32 32 + 3 = 35 So, 8(3/4) acres is the same as 35/4 acres.Calculate rate per hour: Calculate the rate per hour. To find the rate per hour, divide the number of acres harvested (35/4) by the fraction of the hour during which the harvesting occurs (5/6). The rate is (35/4) / (5/6).Divide fractions: Perform the division of fractions. To divide by a fraction, multiply by its reciprocal. The reciprocal of 5/6 is 6/5. Now multiply (35/4) by (6/5). (35/4) * (6/5) = (35 * 6) / (4 * 5)Calculate multiplication: Calculate the multiplication. 35 * 6 = 210 4 * 5 = 20 So, (35 * 6) / (4 * 5) = 210/20Simplify the fraction: Simplify the fraction. 210/20 can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 10. 210 ÷ 10 = 21 20 ÷ 10 = 2 So, 210/20 simplifies to 21/2.Convert to mixed number: Convert the improper fraction to a mixed number (if necessary). 21/2 is an improper fraction. To convert it to a mixed number, divide 21 by 2. 21 ÷ 2 = 10 with a remainder of 1. So, 21/2 acres is the same as 10(1/2) acres. However, since we are looking for the rate per hour, we can leave it as an improper fraction.

Darcy harvests $8 \frac{3}{4}$ acres of corn every $\frac{5}{6}$ of an hour. Darcy harvests corn at a constant rate. $\newline$ How many acres does she harvest per hour? $\newline$ acres per hour

Full solution

More problems from GCF and LCM: word problems

Related topics

Darcy harvests 834 8 \frac{3}{4} 843​ acres of corn every 56 \frac{5}{6} 65​ of an hour. Darcy harvests corn at a constant rate.\newlineHow many acres does she harvest per hour?\newlineacres 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. $\newline$ How many acres does she harvest per hour? $\newline$ acres per hour