Working together, Melissa and Jing can mow a lawn in 5 hours. It would take Melissa 8 hours to do the job alone.
| | Rate (part/hour) | Time (hours) | Part of Lawn Mowed |
| :------ | :--------------- | :----------- | :----------------- |
| Melissa | [tex]$\frac{1}{8}$[/tex] | 5 | [tex]$\frac{5}{8}$[/tex] |
| Jing | r | 5 | 5r |
What is the value of [tex]$r$[/tex], the part of the lawn that Jing could complete in 1 hour?
A. 0.075
B. 0.125
C. 0.375
D. 0.625
Answer (1)
Set up the equation representing the combined work of Melissa and Jing: 8 5 + 5 r = 1 .
Isolate the term with r by subtracting 8 5 from both sides: 5 r = 8 3 .
Solve for r by dividing both sides by 5: r = 40 3 .
Convert the fraction to a decimal to find the value of r : 0.075 .
Explanation
Problem Analysis Let's analyze the problem. We know that Melissa and Jing can mow a lawn together in 5 hours. Melissa's individual rate is 8 1 lawns per hour. We need to find Jing's rate, r , which represents the fraction of the lawn Jing can mow in 1 hour. The table provides the necessary information to set up an equation.
Setting up the Equation Since Melissa and Jing work together, the sum of the fractions of the lawn they each mow in 5 hours must equal 1 (the whole lawn). Melissa mows 8 5 of the lawn in 5 hours, and Jing mows 5 r of the lawn in 5 hours. Therefore, we can write the equation: 8 5 + 5 r = 1
Isolating the Term with r Now, let's solve the equation for r . First, subtract 8 5 from both sides of the equation: 5 r = 1 − 8 5 5 r = 8 8 − 8 5 5 r = 8 3
Solving for r Next, divide both sides of the equation by 5: r = 5 8 3 r = 8 3 × 5 1 r = 40 3
Finding the Decimal Value Finally, convert the fraction to a decimal: r = 40 3 = 0.075 Therefore, Jing can mow 0.075 of the lawn in 1 hour.
Examples
Imagine you're organizing a team to complete a project. Melissa can complete 8 1 of the project per hour, and you want to figure out how much Jing contributes per hour so that together, they finish the project in 5 hours. This problem demonstrates how understanding individual rates and combining them can help in project planning and resource allocation. By calculating each person's contribution, you can effectively manage tasks and ensure timely completion.
