SOLUTION: A father and his son can clean the house together in 8 hours. When the son works alone, it takes him an hour longer to clean than it takes his dad alone. Find how long it takes the

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Question 1089560: A father and his son can clean the house together in 8 hours. When the son works alone, it takes him an hour longer to clean than it takes his dad alone. Find how long it takes the son to clean alone.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
FATHER                 

SON                    

FATHER AND SON

-

-


ALTERNATIVE:
FATHER                 
SON                    
FATHER AND SON


-




-


-



-
, 
close enough to

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Let x be the time in hours for son to complete the job working alone.
Then the time for the father is x-1 hours.

The son's    rate of work is        of the job per hour.

The father's rate of work is    of the job per hour.

Their combined rate of work is  .

From the other side, the condition says that their combined rate of work is    of the job per hour.


It gives you an equation 

 = .


To solve it, multiply both sides by 8x*(x-1). You will get

8(x-1) + 8x = x*(x-1).

Simplify and solve for x:

x^2 - 17x + 8 = 0,

 =  =  = .

Only positive root works: x =  = 16.5 hours = 16 hours and 30 minutes (approximately).

Check.   = 0.1251;    = 0.125.

               Check is good !.

Answer.  It will take approximately 16.5 hours for the son to make this job working alone.

Solved.


It is a typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".



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