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The equation that can be used to find the time t, in hours, it would take Johnson and Nathan to tile a 100 square foot area together is 3.9375 hours, which approximates to 4 hours.
How are number of people to time needed to complete a task related?
More people to do a task means less time it will take.
Less people to do a task means more time it will take.
Thus, they are inversely related.
If x men take y time for a work,(assume all men have same strength)
We can define a constant as "Manpower" needed for doing that specific work.
Let we define:
Manpower needed for a work = y + y + y + .. + y = Time per man × count of men
Manpower needed for a work = xy
For this case, we're specified that:
- Work in consideration = Tiling 100 sq. foot floor
- Time it takes by Johnson to do this work = 7 hours
- Time it takes by Nathan to do this work = 9 hours
So, we see that strength of Johnson and Nathan are different.
Let the general manpower (from some frame of a general public or any third frame) needed by this work be M.
Then, Johnson delivers M manpower in 7 hours or M/7 manpower in one hour.
In the similar way, Nathan delivers M/9 manpower per hour.
Thus, if Nathan and Johnson work together, they can deliver: [tex]\dfrac{M}{9} + \dfrac{M}{7} = M\dfrac{9+7}{63} = \dfrac{16M}{63}[/tex] manpower per hour.
Let it takes them together h hours to complete the work.
That means, in 'h' hours, their together work power will accumulate to M manpower.
Or, we can say:
[tex]h \times \dfrac{16M}{63} = M\\\\h = \dfrac{63M}{16M} = \dfrac{63}{16} = 3.9375[/tex]
Thus, the equation that can be used to find the time t, in hours, it would take Johnson and Nathan to tile a 100 square foot area together is 3.9375 hours, which approximates to 4 hours.
Learn more about work and time here:
https://brainly.com/question/1063042
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