SOLUTION: A man can do a piece of work in 9 hours. After he worked 3 hours alone, he was joined by his son, and they finished the job in 4 1/2 hours. How many hours would it take the son to

Question 524066: A man can do a piece of work in 9 hours. After he worked 3 hours alone, he was joined by his son, and they finished the job in 4 1/2 hours. How many hours would it take the son to do the job alone?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
The father is able to the job in 9 hr or 1/9 of the job per hr.
The father worked for 4.5 hr = 9/2 hr.
The son only worked for 4.5-3=1.5 hr or 3/2 hr.
.
1/9*9/2 + 1/x*3/2 = 1 whole job
.
1/9*9/2 = 9/18 = 1/2
1/x*3/2 = 3/(2x)
.
1/2 + 3/(2x) = 1
.
(2x + 6)/(4x) = 1
.
2x + 6 = 4x
.
2x = 6
.
x = 3
.
The son can do the job in 3 hr.
.
Check this answer.
.
The father did 1/3 of the job before the son started.
The father did 1/9*3/2 = 3/18 = 1/6 of the job after the son arrived.
The father tid 1/3+1/6 = 2/6+1/6 = 3/6 = 1/2 of the job in total.
The son did 1/3*3/2 = 1/2 of the job.
1/2+1/2=1.
Correct.
.
Done.

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