SOLUTION: A,B and C can do a job in 4 days . B can do it in 9 days and C can do it in 8 days . How long would it take A to do it himself ?

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: A,B and C can do a job in 4 days . B can do it in 9 days and C can do it in 8 days . How long would it take A to do it himself ?       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1139010: A,B and C can do a job in 4 days . B can do it in 9 days and C can do it in 8 days . How long would it take A to do it himself ?
Found 3 solutions by VFBundy, MathTherapy, ikleyn:
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
A, B, and C, working together, can do 1/4 of the job per day.
A, working alone, can do 1/A of the job per day. (We are trying to figure out what A is.)
B, working alone, can do 1/9 of the job per day.
C, working alone, can do 1/8 of the job per day.

"A, B, and C, working together, can do 1/4 of the job per day.":

1/A + 1/9 + 1/8 = 1/4

Common denominator for left side of equation is: (A)(9)(8) = 72A

Set up the equation using 72A as common denominator on left side of equation, then simplify:

(1*9*8)/72A + (1*8*A)/72A + (1*9*A)/72A = 1/4

72/72A + 8A/72A + 9A/72A = 1/4

(72 + 8A + 9A)/72A = 1/4

(72 + 17A)/72A = 1/4

Cross-multiply:

4(72 + 17A) = 1(72A)

Simplify:

288 + 68A = 72A

288 = 4A

A = 72

It will take A 72 days to do the job himself.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A,B and C can do a job in 4 days . B can do it in 9 days and C can do it in 8 days . How long would it take A to do it himself ?
Let time A takes be A

Then when A, B, and C work together, they perform: matrix%281%2C6%2C+1%2FA%2C+%22%2C%22%2C+1%2F9%2C+%22%2C%22%2C+and%2C+1%2F8%29 of work, respectively 

Then we get: matrix%281%2C3%2C+4+%2A+%281%2FA+%2B+1%2F9+%2B+1%2F8%29%2C+%22=%22%2C+1%29

matrix%281%2C3%2C+4%2FA+%2B+4%2F9+%2B+1%2F2%2C+%22=%22%2C+1%29

4(18) + 4(2A) + 9A = 18A ------- Multiplying by LCD, 18A

72 + 8A + 9A = 18A

72 = 18A - 17A

Time A takes to do the job, alone, or highlight_green%28matrix%281%2C4%2C+A%2C+%22=%22%2C+72%2C+days%29%29

Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let "a" be the  A's rate  of work.


From the condition,  rate of work for B is 1%2F9 and rate of work for C is 1%2F8.


Also, we are given that 


    a + 1%2F9 + 1%2F8 = 1%2F4.


Therefore,


    a = 1%2F4 - 1%2F8 - 1%2F9 = 18%2F72 - 9%2F72 - 8%2F72 = 1%2F72.


Thus, A's rate of work is  1%2F72,  which means that A can complete the job in 72 days, working alone.

Solved.

----------------

It is a standard and 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".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.