SOLUTION: Andrew can paint the​ neighbor's house 4 times as fast as Bailey. The year Andrew and Bailey worked​ together, it took them 9 days. how long would it take andrew?

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Question 1115357:
Andrew can paint the​ neighbor's house 4 times as fast as Bailey. The year Andrew and Bailey worked​ together, it took them 9 days. how long would it take andrew?
How long would it take bailey?
Found 3 solutions by stanbon, greenestamps, ikleyn:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Andrew can paint the​ neighbor's house 4 times as fast as Bailey. The year Andrew and Bailey worked​ together, it took them 9 days. how long would it take andrew?
How long would it take bailey?
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Bailey time = 4x days/job ; rate = 1/(4x) job/days
-------
Andrew time = x days/job ; rate = 1/x job/days
----
Together time = 9 days/job ; rate = 1/9 job/day
------
Equation:
rate + rate = together rate
1/(4x) + 1/x = 1/9
Multiply thru by 36x to get:
9 + 36 = 4x
4x = 45
x = 45/4
---
Ans: Bailey time = 4(45/4) = 45 days
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Cheers,
Stan H.
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Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Since Andrew works 4 times as fast as Bailey, when they work together Andrew does 4/5 of the work and Bailey does 1/5.

Working together, they took 9 days to do the job.

The amount of time Andrew would take working alone is days.

The amount of time Bailey would take working alone is days.
Answer by ikleyn(52812)   (Show Source): You can put this solution on YOUR website!
.
Let  "r"  be the Bailey's rate of work.


Then  Andrew's  rate of work  is 4r,  according to the condition.


Hence, the combined rate ow work is 5r,  and the problem says that


    5r9 = 1   (they make the job in 9 days working together).


Hence,  r = ,   which means that Bailey makes the job in 45 days.


It implies that Andrew makes the job in   days.

Solved.

--------------------
It is a typical and standard 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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