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Lena [83]
4 years ago
11

Five people can mow a lawn in 12 hours. How many more people are needed to mow the lawn in just 3 hours, assuming each person mo

ws at the same rate?
Mathematics
2 answers:
Bumek [7]4 years ago
6 0
If five people can do it in 12 hours, then you divide and see how long it takes each person. then you figure the rate for how many hours per person. then you figure out how many peopl it takes to do it all in 3 hours
inna [77]4 years ago
6 0

The number of people mowing and the time required to mow are inversely proportional. Letting n be the number of people and t be the amount of time, we have nt = (5)(12)= 60 because 5 people can mow a lawn in 12 hours. If m people can mow the lawn in 3 hours, then we must have m(3) = 60, so m=20. Therefore, we need to add 20-5 = 15 people to the job.

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The area of the garden enclosed by the fencing is

A(x, y) = xy

and is constrained by its perimeter,

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Solve for x in the constraint equation:

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Substitute this into the area function to get a function of one variable:

A(200 - 2y, y) = A(y) = 200y - 2y²

Differentiate A with respect to y :

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Find the critical points of A :

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Compute the second derivative of A:

d²A/dy² = -4 < 0

Since the second derivative is always negative, the critical point is a local maximum.

If y = 50, then x = 200 - 2•50 = 100. So the farmer can maximize the garden area by building a (100 ft) × (50 ft) fence.

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