SOLUTION: 3. Six adults can complete a piece of work in one day while 5 children would take 2 days to complete the same piece of work. Using this ratio, think about the following problem. Fo

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Question 437909: 3. Six adults can complete a piece of work in one day while 5 children would take 2 days to complete the same piece of work. Using this ratio, think about the following problem. Forty-four adults can build a tower in 5 days. How long will 40 adults and 80 children take to build a tower?
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
1 child would take 10 days to do a job
1 adult would take 6 days to do a job
---------------------
Building the tower, let = the rate that
children work.
Let = the rate that an adult works
44 adults in 5 days to build a tower
is adults/day to build a tower





The rate for 40 adults is
The rate for 80 children is
---------------------
Add the rates to get their rate working together
(1 tower in d days)

Multiply both sides by




It will take 50 adults and 80 children 2.5 days to build a tower
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Six adults can complete a piece of work in one day while 5 children would take 2 days to complete the same piece of work. Using this ratio, think about the following problem. Forty-four adults can build a tower in 5 days. How long will 40 adults and 80 children take to build a tower? 

Six adults can complete a piece of work in one day 

So 1 adult can complete a piece of work in 6 days.

So 1 adult's rate is 1/6 jobs per day

5 children would take 2 days to complete the same piece of work. 

So 1 child can complete the same piece of work in 10 days

So 1 child's rate is 1/10 jobs per day

Question: The child's rate of 1/10 jobs per day is what 
fraction of the adult's rate of 1/10 jobs per day?

Answer: divide 1/10 by 1/6:  1/10÷1/6 = 1/10×6/1 = 6/10 = 3/5

So a child's rate is 3/5 of (times) an adult's rate. 

Forty-four adults can build a tower in 5 days.

So 1 adult can build a tower in 44×5 or 220 days

So 1 adult's rate is 1/220 towers per day.

So 1 child's rate is 3/5×1/220 = 3/1100 towers per day.

So 40 adults' combined rate is 40×(1/220) = 40/220 = 4/22 = 
2/11 towers per day

So 80 children's combined rate is 80×3/1100 = 12/55 towers 
per day.

So 40 adults' and 80 children's combined rate is 2/11 + 12/55 
towers per day

That's 2/11+12/55 = 10/55 + 12/55 = 22/55 = 2/5 towers per 
day.

So to build 1 tower we divide 1 tower by 2/5 towers per day:

1÷2/5 = 1×5/2 = 5/2 = 2 1/2 days.

Edwin
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