SOLUTION: A man can do a job in 9 days and his son can do the same job in 16 days. They start working together. After 4 days, the son leaves and the father finishes the job alone. How many d

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A man can do a job in 9 days and his son can do the same job in 16 days. They start working together. After 4 days, the son leaves and the father finishes the job alone. How many d      Log On


   

Question 66887: A man can do a job in 9 days and his son can do the same job in 16 days. They start working together. After 4 days, the son leaves and the father finishes the job alone. How many days did it take the man to finish the job alone?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
A man can do a job in 9 days and his son can do the same job in 16 days. They start working together. After 4 days, the son leaves and the father finishes the job alone. How many days did it take the man to finish the job alone?
The man can do 1/9 of the job per day
The boy can do 1/16 of the job per day
Both working together, they can do 1/9+1/16 of the job per day which equals:
1/9+1/16----LCM is 144
(16+9)/144=25/144
Both working together they can do 25/144 of the job per day
In 4 days they will have done 4(25/144) of the job
4/(25/144)=25/36 of the job
36/36-25/36 =11/36 the amount of the job remaining afer 4 days
The man can do 1/9 (or 4/36) of the job per day and there's 11/36 of the job left
So it will take the man working alone (11/36)/(4/36) days to finish
(11/36)/(4/36)=(11/36)(36/4)=11/4 =2.75 days
So it will take the man working alone 2.75 days to finish

This looks like it, unless I goofed somewhere.

Hope this helps----ptaylor