SOLUTION: A father and his son can dig a well if the father work 6 hours and his son does 12 hours or they can do the job if father works 9 hours and the son works 8 hours. How long will it

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A father and his son can dig a well if the father work 6 hours and his son does 12 hours or they can do the job if father works 9 hours and the son works 8 hours. How long will it       Log On


   

Question 1080507: A father and his son can dig a well if the father work 6 hours and his son does 12 hours or they can do the job if father works 9 hours and the son works 8 hours. How long will it take for the son to dig the well alone?
Answer by ikleyn(52876) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let f = the father's rate of work and s = the son's rate of work.


The first equation is

6f + 12s = 1     (1)   

The second equation is

9f + 8s = 1.     (2).


To solve the system, multiply eq.(1) by 3; multiply eq.(2) by 2 and then subtract. You will have

18f + 36s = 3,   (1')
18f + 16s = 2    (2')
------------------------Subtract

====> 20s = 1   --->  s = 1/20.


Thus the son's rate of work is 1%2F20 which means that he will complete the job in 20 hours working alone.

Solved.