- The work rates are combined: (Melissa's rate + Jing's rate) × time = total work.
- The equation is setup: \(5 \times (\frac{1}{8} + r) = 1\).
- Simplifying the expression leads to: \(5r = \frac{3}{8}\).
- Solving for \(r\) gives: \(r = \frac{3}{40} = \boxed{0.075}\).
Explanation
- Analysis of the Problem
To find the rate at which Jing mows the lawn, we identify the work rates and the total time taken. Melissa and Jing work together for 5 hours to complete one whole lawn. Melissa's rate is given as \(\frac{1}{8}\) of the lawn per hour. Let \(r\) be Jing's rate in lawns per hour. The total work done by both together in 5 hours equals 1 (a complete lawn).
- Setting up the Equation
We set up the work equation based on the given information: the sum of the work done by Melissa and Jing equals 1.
\[5 \times \left(\frac{1}{8} + r\right) = 1\]
Distributing the 5 gives:
\[\frac{5}{8} + 5r = 1\]
- Solving for the Rate \(r\)
To isolate \(5r\), we subtract \(\frac{5}{8}\) from both sides:
\[5r = 1 - \frac{5}{8}\]
\[5r = \frac{8}{8} - \frac{5}{8} = \frac{3}{8}\]
Now, divide by 5 to find \(r\):
\[r = \frac{3}{8} \div 5 = \frac{3}{8 \times 5} = \frac{3}{40}\]
- Calculation and Final Answer
Finally, we convert the fraction \(\frac{3}{40}\) into a decimal:
\[r = \frac{3}{40} = 0.075\]
Thus, Jing completes 0.075 of the lawn in 1 hour, which corresponds to the first option. The final answer is \(\boxed{0.075}\).
Examples
Knowing how to combine work rates is essential for project management and resource allocation. For example, if two employees work together to complete a task, calculating their individual rates allows a manager to determine how long it will take for them to finish the job, or to estimate if additional help is needed to meet a deadline. This mathematical approach helps in planning schedules and optimizing productivity in any collaborative environment.