suppose that the amount of time it takes to build a highway vadies directly with the length of the highway and inversely with the number of workers. suppose also that it takes 300 workers 22 week to build 24 miles of highway. how long will it take 225 to build 27 miles of highway

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25-10-2022
Mathematics

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suppose that the amount of time it takes to build a highway vadies directly with the length of the highway and inversely with the number of workers. suppose also that it takes 300 workers 22 week to build 24 miles of highway. how long will it take 225 to build 27 miles of highway

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MaiyanaK505632 MaiyanaK505632 · Answer 1 · 2022-10-25T17:11:20+02:00

[tex]\begin{gathered} \text{Let the length of the highway be represented by L} \\ \text{Let the Time it takes be represented by: T} \\ \text{Let the number of workers be: N} \\ T\text{ }\propto\frac{L}{N} \\ \\ T\text{ =}\frac{KL}{N}------------(1) \\ \\ K\text{ = }\frac{TN}{L}\text{ = }\frac{22\text{ }\times300}{24}\text{ = 275} \\ T\text{ = ?, N = 225},\text{ L = 27} \\ using\text{ equation(1)} \\ T\text{ = }\frac{KL}{N}\text{ = }\frac{275\times27}{225}\text{ = }\frac{7425}{225}\text{ = 33w}eeks \end{gathered}[/tex]