Is there some other way I can explain this to my 8th grader.
Five editors finish a project in 3 1/2 weeks. How many editors are needed to complete the same project in 1 1/6 weeks
didn't my solution in the related question below do the job?
think of it in terms of "workweeks"
Number of total workweeks needed is 5(3.5) or 17.5
that is workweeks = number of workers x number of weeks
so number of workers = workweeks/number of weeks
= 17.5/(7/6)
= 17.5(6/7) = 15
To explain this problem to your 8th grader, you can break it down into smaller steps.
Step 1: Understand the scenario
There is a project that needs to be completed, and a group of editors is working on it. The first piece of information tells us that five editors finished the project in 3 1/2 weeks.
Step 2: Analyze the problem
Now, we need to find out how many editors are needed to complete the same project in a shorter duration, specifically 1 1/6 weeks.
Step 3: Identify the formula
To solve this problem, we can use the concept of "work", which is the amount of progress made in a given time. The formula for this is:
Work = Rate * Time
Step 4: Calculate the initial rate
Based on the first scenario, we know that five editors completed the project in 3 1/2 weeks. To find the initial rate at which they worked, we divide the total work by the time taken:
Rate = Work / Time
Rate = 1 / 3.5
Step 5: Calculate the amount of work
The amount of work for the project remains the same, regardless of the time duration. We can represent this as the total work completed in the first scenario:
Work = 1
Step 6: Calculate the new rate
Now, we need to determine how many editors are needed to complete the project in 1 1/6 weeks. Let's denote the required number of editors as 'x'. The rate for this scenario is:
Rate = 1 / 1.1667
Step 7: Set up the equation and solve for 'x'
Equating the two rates, we get:
1 / 3.5 = 1 / 1.1667*x
To solve for 'x', we can cross-multiply and then solve the resulting equation for 'x':
3.5 * 1.1667 * x = 1
4.08185 * x = 1
x = 1 / 4.08185
x ≈ 0.24491
Step 8: Interpret the answer
The answer suggests that approximately 0.24491 editors are needed to complete the project in 1 1/6 weeks. However, since we cannot have a fraction of an editor, we can round up the answer to 1 editor. Therefore, approximately one editor is needed to complete the project in 1 1/6 weeks.
Note: The rounding in the final step is done to find a practical solution, as it is not feasible to have a fraction of an editor.