SOLUTION: it takes you 8 hours to dig a hole. it takes you and your brother 5 hours to dig that same hole together. if your brother were to dig the hole by himself, how long would it take hi

Algebra ->  Rate-of-work-word-problems -> SOLUTION: it takes you 8 hours to dig a hole. it takes you and your brother 5 hours to dig that same hole together. if your brother were to dig the hole by himself, how long would it take hi      Log On


   

Question 895935: it takes you 8 hours to dig a hole. it takes you and your brother 5 hours to dig that same hole together. if your brother were to dig the hole by himself, how long would it take him?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
It takes you 8 hours to dig a hole.
Your rate is 1 hole per 8 hours or 

matrix%281%2C2%2C1%2Chole%29%2Fmatrix%281%2C2%2C8%2Chours%29 = matrix%281%2C2%2C1%2F8%2Chole%2Fhour%29

if your brother were to dig the hole by himself, how long would it take him?
Let the answer be x hours.
Your brother's rate is 1 hole per x hours or 

matrix%281%2C2%2C1%2Chole%29%2Fmatrix%281%2C2%2Cx%2Chours%29 = matrix%281%2C2%2C1%2Fx%2Chole%2Fhour%29

it takes you and your brother 5 hours to dig that same hole together.

Then your combined rate is 1 hole per 5 hours or 

matrix%281%2C2%2C1%2Chole%29%2Fmatrix%281%2C2%2C5%2Chours%29 = matrix%281%2C2%2C1%2F5%2Chole%2Fhour%29

The equation comes from:

%28matrix%285%2C1%2CYour%2Chole-digging%2Crate%2C+in%2C+%22hole%2Fhour%22%29%29%22%22%2B%22%22 %22%22=%22%22 %28matrix%286%2C1%2CYour%2Ccombined%2C+hole-digging%2C+rate%2C+in%2C+%22hole%2Fhour%22%29%29

So

   matrix%281%2C2%2C1%2F8%2Chole%2Fhour%29%22%22%2B%22%22matrix%281%2C2%2C1%2Fx%2Chole%2Fhour%29 %22%22=%22%22 matrix%281%2C2%2C1%2F5%2Chole%2Fhour%29

      1%2F8%22%22%2B%22%221%2Fx %22%22=%22%22 1%2F5

Multiply through by LCD = 40x


      5x%22%22%2B%22%2240 %22%22=%22%22 8x
             
            -3x%22%22=%22%22-40

             x%22%22=%22%22%28-40%29%2F%28-3%29

             x%22%22=%22%2240%2F3

             x%22%22=%22%2213%261%2F3hours

Edwin