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Johnson can tile a 100 square foot floor in 7 hours. Nathan can tile the same area in 9 hours. Enter an equation that can be used to find the time in hours,t it would take Johnson and Nathan to tile a 100 square foot area together.

Sagot :

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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