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Working​ together, it takes two roofers 12 hours to put a new roof on a portable classroom. if the first roofer can do the job by himself in 16 ​hours, how many hours will it take the second roofer to do the job by​ himself?

Respuesta :

DeanR

Let r and s be the respective rates in roofs per hour.


[tex]12 = 1/(r+s)[/tex]


[tex]r+s=1/12[/tex]


[tex]s= -r + \frac 1 {12}[/tex]


[tex]16=1/r[/tex]


[tex]r=1/16[/tex]


[tex]s= - \frac 1{16} + \frac 1 {12}[tex] = -\frac{3}{48} + \frac{4}{48} = \frac{1}{48}[/tex]


The second worker's rate is 1/48 roofs per hour or one roof every 48 hours.




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