SOLUTION: A farmer plows the field using a tractor in 5 days. His father can do the same job in 9 days. How many days will it take them working together?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A farmer plows the field using a tractor in 5 days. His father can do the same job in 9 days. How many days will it take them working together?      Log On


   

Question 896101: A farmer plows the field using a tractor in 5 days. His father can do the same job in 9 days. How many days will it take them working together?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
A farmer plows the field using a tractor in 5 days.
The farmer's rate is 1 field per 5 days or 

matrix%281%2C2%2C1%2Cfield%29%2Fmatrix%281%2C2%2C5%2Cdays%29 = matrix%281%2C2%2C1%2F5%2Cfield%2Fday%29

His father can do the same job in 9 days.
His father's rate is 1 field per 9 days or 

matrix%281%2C2%2C1%2Cfield%29%2Fmatrix%281%2C2%2C9%2Cdays%29 = matrix%281%2C2%2C1%2F9%2Cfield%2Fday%29

How many days will it take them working together?
Let the answer be x days.

Then their combined rate is 1 field per x days or 

matrix%281%2C2%2C1%2Cfield%29%2Fmatrix%281%2C2%2Cx%2Cdays%29 = matrix%281%2C2%2C1%2Fx%2Cfield%2Fday%29

The equation comes from:

%22%22%2B%22%22 %22%22=%22%22 %28matrix%286%2C1%2CTheir%2Ccombined%2C+plowing%2C+rate%2C+in%2C+%22field%2Fday%22%29%29

So

   matrix%281%2C2%2C1%2F5%2Cfield%2Fday%29%22%22%2B%22%22matrix%281%2C2%2C1%2F9%2Cfield%2Fday%29 %22%22=%22%22 matrix%281%2C2%2C1%2Fx%2Cfield%2Fday%29

      1%2F5%22%22%2B%22%221%2F9 %22%22=%22%22 1%2Fx

Multiply through by LCD = 45x


      9x%22%22%2B%22%225x %22%22=%22%22 45
             
            14x%22%22=%22%2245

             x%22%22=%22%2245%2F14

             x%22%22=%22%223%263%2F14days

Edwin