SOLUTION: 12 Workers can finish a third of a house in 15 days. How many workers must be added to finish the rest of the house in the next 18 days? Could you please explain and draw some

Question 1054311: 12 Workers can finish a third of a house in 15 days. How many workers must be added to finish the rest of the house in the next 18 days?
Could you please explain and draw some diagrams or pictures which could help me understand? Thanks. (Or anything that would help me in solving unit rate problems)
Found 4 solutions by Boreal, josmiceli, MathTherapy, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
12 workers do 1/3 of a house in 15 days
in 1 day 12 workers do 1/45 of a house
1 worker does 1/540 of a house in a day, since 12 workers do 1/45th of a house (12/540)
want to know how many workers do 2/3 of a house in 18 days. Let the number = x.
18x/540=2/3 of a house. 18x is 18 days*x number of workers.
cross multiply
1080=54x
x=20
8 more workers must be added, since there are 12 to begin with.
--------------------
Check
12 workers can do 1/3 of a house in 15 days or the whole house in 45 days.
That means that there are 540 worker-days required to build the house.
12*15=180 worker days, the 1/3 of a house.
The 20 workers*18 days is 360 worker days, and that is 2/3 of the house.

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
I use a step by step logic method
( not the only way to do this )
--------------------------------
12 workers take 15 days to finish 1/3 of a house
--------------------------------------------
After 1/3 of the house is finished, I want to know
how many workers can finish the remaining 2/3
of the house in 18 aditional days.
--------------------------------------------
It will take twice as many workers do do twice as
much work ( 2/3 of a house ) in the same time, so
---------------------------------------------
24 workers take 15 days to do 2/3 of a house
---------------------------------------------
If wokers only have 1/5 of this amount of time to do
the same amount of work ( 2/3 of a house ), then
it will take 5 times as many workers, so
----------------------------------------------
120 workers take 3 days to do 2/3 of a house
-----------------------------------------------
Now if workers can take 6 times as long to do the
same amount of work, then it will only require 1/6
as many workers, so
-----------------------------------------------
20 workers take 18 days to do 2/3 of a house
( the remaining 2/3 )

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

12 Workers can finish a third of a house in 15 days. How many workers must be added to finish the rest of the house in the next 18 days?
Could you please explain and draw some diagrams or pictures which could help me understand? Thanks. (Or anything that would help me in solving unit rate problems)

Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
12 Workers can finish a third of a house in 15 days. How many workers must be added to finish the rest of the house in the next 18 days?
Could you please explain and draw some diagrams or pictures which could help me understand? Thanks. (Or anything that would help me in solving unit rate problems)
~~~~~~~~~~~~~~~~~~~~~

Since 12 Workers can finish a third of a house in 15 days, the rate of work of one worker is r = = of the house per day. Let x = "How many workers must be added to finish the rest of the house in the next 18 days" Then we have this equation = . Then x+12 = = {{(2/3)*30}}} = 20. Hence, x = 20-12 = 8. Answer. 8 workers must be added to 12 workers.

There is a variety of solved joint-work problems with detailed explanations for you in the lessons
    - Rate of work problems
    - 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
in this site.

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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