SOLUTION: A farmer can fplow the filed in 8 days. After working for 3 days,the son joins him amd together the plow the field in 3 more days. How many days will it require for the son to plow

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A farmer can fplow the filed in 8 days. After working for 3 days,the son joins him amd together the plow the field in 3 more days. How many days will it require for the son to plow      Log On


   

Question 765058: A farmer can fplow the filed in 8 days. After working for 3 days,the son joins him amd together the plow the field in 3 more days. How many days will it require for the son to plow the field alone?
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
THREE MAIN PARTS OF THE FIELD-PLOWING.

FATHER FOR 3 DAYS

Rate is 1%2F8 job per day. We can find how much job was done and what still needs to be done.
%281%2F8%29%2A3 job was done.
1-%281%2F8%29%2A3 job still needs to be done.
That is highlight%285%2F8%29 job still needs to be done.

FATHER & SON FINISH

They plow the field in 3 days, suggesting they finished the field. We do not know their combined rate nor the son's but we can use a variable for the son's rate.
%281%2F8%2Br%29%2A3=5%2F8 using r for the son's rate of work, allows us to find the son's rate if he were to work alone.
Solve for r.
3r%2B3%2F8=5%2F8
3r=5%2F8-3%2F8
3r=1%2F4
highlight%28r=1%2F12%29 which means, the son could plow the field alone in 12 days.

SON ALONE TO FINISH
Right! Already answered. The rate for the son is 1/12 job per day or as the reciprocal, 12 days to plow the field himself.