SOLUTION: Jay can do a painting job in 2/3 as many days as Chris can, and Chris can do it in 3/4 as many days as Araceli can. If all three work together, they can do it in 36/13 days. In how

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Question 1199268: Jay can do a painting job in 2/3 as many days as Chris can, and Chris can do it in 3/4 as many days as Araceli can. If all three work together, they can do it in 36/13 days. In how many days can each of them alone do the work?
Found 4 solutions by ankor@dixie-net.com, josgarithmetic, greenestamps, ikleyn:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
Jay can do a painting job in 2/3 as many days as Chris can,
and Chris can do it in 3/4 as many days as Araceli can.
If all three work together, they can do it in 36/13 days.
In how many days can each of them alone do the work?
:
let a = time required by A do the job
then
(2/3)*(3/4) = (1/2)a = J's time to do the job
and
(3/4)a = C's time
We can use decimals with these two fractions, .5 and .75 (less tedious)
lets try using 36/13 = 2.77 for time working together
let 1 = the completed job
+ + = 1
multiply by 3a, cancel the denominators, gets rid of the fractions
6(2.77) + 4(2.77) + 3(2.77) = 3a
16.62 + 11.08 + 8.31 = 3a
totals 36.01,round it down to 36
3a = 36
a = 12 hrs is A's time
then
.5(12) = 6 hrs is J's time
and
.75(12) = 9 hrs is C's time
:
You can confirm this in the original equation, comes to slightly more than 1 because 2.77 is actually 2.76923 (36/13)
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Araceli, d days 1 job
Chris, days 1 job
Jay, days 1 job

The three combined need days to do 1 job.
----------simplify and solve first for d.

STEPS POSSIBLE-----------





------------Time for Araceli, working alone.

You can use this to find time for Chris and for Jay.
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Chris can do it in 3/4 as many days as Araceli can:
let 4x = days Araceli takes
then 3x = days Chris takes

Jay can do it in 2/3 as many days as Chris can:
then 2x = days Jay takes

The fraction of the job Araceli does in 1 day is 1/(4x)
The fraction of the job Chris does in 1 day is 1/(3x)
The fraction of the job Ray does in 1 day is 1/(2x)

Together in 1 day the fraction of the job the three together do is



That means the number of days it takes them to do the job together is

The number of days they take to do the job is 36/13, so

36/13 = 12x/13 --> x = 3

ANSWERS:
# of days for Araceli alone = 4x = 12
# of days for Araceli alone = 3x = 9
# of days for Araceli alone = 2x = 6
Answer by ikleyn(52812)   (Show Source): You can put this solution on YOUR website!
.
Jay can do a painting job in 2/3 as many days as Chris can,
and Chris can do it in 3/4 as many days as Araceli can.
If all three work together, they can do it in 36/13 days.
In how many days can each of them alone do the work?
~~~~~~~~~~~~~~ 

Let "a" be the Araceli's rate of work.


Then Chris' rate of work is  , and Jay's rate of work is .


Their combined rate of work is then 

    a +  +  = a +  + 2a =  = .


From the other side, their combined rate of work is  .


It gives us this equation

     = .


From this equation,  a = .


Thus Araceli can make the job in 12 days, working alone; Cris can make it in   = 9 days
and Jay can make it in   = 6 days.    ANSWER

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.



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