SOLUTION: Pedro can do a piece work in 4 days,while Alan can do a piece of work in 5 days. In how many days can both finish the work, if they work together?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Pedro can do a piece work in 4 days,while Alan can do a piece of work in 5 days. In how many days can both finish the work, if they work together?      Log On


   

Question 883383: Pedro can do a piece work in 4 days,while Alan can do a piece of work in 5 days. In how many days can both finish the work, if they work together?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Pedro can do a piece work in 4 days,
So Pedro's rate is matrix%281%2C2%2C1%2Cjob%29%2Fmatrix%281%2C2%2C4%2Cdays%29%22%22=%22%22matrix%281%2C2%2C1%2F4%2Cjob%2F%28day%29%29

while Alan can do a piece of work in 5 days,
So Alan's rate is matrix%281%2C2%2C1%2Cjob%29%2Fmatrix%281%2C2%2C5%2Cdays%29%22%22=%22%22matrix%281%2C2%2C1%2F5%2Cjob%2F%28day%29%29

In how many days can both finish the work, if they work together?
Let that be x days.

So their combined rate is matrix%281%2C2%2C1%2Cjob%29%2Fmatrix%281%2C2%2Cx%2Cdays%29%22%22=%22%22matrix%281%2C2%2C1%2Fx%2Cjob%2F%28day%29%29

The equation comes from:

%28matrix%283%2C1%2C%22Pedro%27s%22%2Cwork%2C+rate%29%29%22%22%2B%22%22%28matrix%283%2C1%2C%22Alan%27s%22%2Cwork%2Crate%29%29 %22%22=%22%22 %28matrix%284%2C1%2Ctheir%2Ccombined%2Cwork%2C+rate%29%29

matrix%281%2C2%2C1%2F4%2Cjob%2F%28day%29%29%22%22%2B%22%22matrix%281%2C2%2C1%2F5%2Cjob%2F%28day%29%29 %22%22=%22%22 matrix%281%2C2%2C1%2Fx%2Cjob%2F%28day%29%29

1%2F4%22%22%2B%22%221%2F5 %22%22=%22%22 1%2Fx

Multiply through by LCD of 20x

5x + 4x = 20
     9x = 20
      x = 20%2F9 or 2%262%2F9 days

Edwin