Bryson is planting green beans. He has already picked $1\frac{1}{8}$ bushels and plants at a rate of $\frac{7}{8}$ of a bushel each hour. The equation $\frac{7}{8}h + 1\frac{1}{8} = 6$ can be used to represent h, the number of hours it will take him to pick 6 bushels. What is the value of h?
A. $4\frac{5}{8}$ hours
B. $5\frac{3}{8}$ hours
C. $5\frac{17}{28}$ hours
D. $8\frac{2}{7}$ hours
Answer (1)
Start with the equation: 8 7 h + 1 = 6 .
Subtract 1 from both sides: 8 7 h = 5 .
Multiply both sides by 7 8 : h = 7 40 .
Convert to a mixed number: h = 5 7 5 .
5 7 5
Explanation
Understanding the Problem Let's break down this word problem step by step to find out how many hours it will take Bryson to pick the green becris!
Setting up the Equation First, we know Bryson has already picked 1 1 = 1 bushel. This is our starting point. He picks at a rate of 8 7 of a bushel each hour. We want to find out how many hours (h) it will take him to pick a total of 6 bushels. The equation that represents this situation is 8 7 h + 1 = 6 .
Isolating the Variable Now, let's solve for h. We start by subtracting 1 from both sides of the equation: 8 7 h + 1 − 1 = 6 − 1 8 7 h = 5
Solving for h To isolate h, we multiply both sides of the equation by the reciprocal of 8 7 , which is 7 8 : 7 8 ⋅ 8 7 h = 5 ⋅ 7 8 h = 7 40
Converting to Mixed Number Now, let's convert the improper fraction 7 40 to a mixed number. We divide 40 by 7: 40 ÷ 7 = 5 with a remainder of 5. So, 7 40 = 5 7 5 . Therefore, it will take Bryson 5 7 5 hours to pick the remaining bushels.
Final Answer The value of h is 5 7 5 hours. Looking at the answer choices, we see that option C, 5 7 5 hours, matches our solution.
Examples
Imagine you're baking cookies for a bake sale. You've already baked 1 batch, and you can bake 8 7 of a batch every hour. If you need to have 6 batches in total, this problem helps you calculate how many more hours you need to bake. Understanding rates and setting up equations like this is useful for managing time and resources in everyday tasks, from cooking to planning projects.
