Suppose that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers. Suppose also that it takes 100 workers 6 weeks to build 4 miles of highway. How many workers would be needed to build 16 miles of highway in 15 weeks?

The number of workers needed will be .

Let

since the time taken is directly proportional to the length of the highway, but inversely proportional to the number of workers, we will have

substitute the values into the formula to find the proportionality constant

now that we have our formula

we can now solve our main problem by substituting the values to find

The number of workers needed to build a highway of in will be

Learn more about direct and inverse proportion here: link

Therefore 160 workers needed to build 16 miles of highway in 15 weeks.

Step-by-step explanation:

Given that,

the amount of time to build a highway varies inversely with the number of workers and varies directly with the length of the highway.

i.e

T= time, L= length of highway and W= number of workers.

So,we can rewrite the above equation

Here, = 100 worker, = 4 miles, = 15 weeks

= ?, = 16 miles, = 15 weeks

        [ Multiply both sides]

Therefore to build 16 miles of highway in 15 weeks 160 workers needed.

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