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

Algebra ->  Rate-of-work-word-problems -> 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      Log On


   

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) About Me  (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 R%5Bc%5D = the rate that
children work.
Let R%5Ba%5D = the rate that an adult works
44 adults in 5 days to build a tower
is +1%2F220 adults/day to build a tower
+R%5Ba%5D%2FR%5Bc%5D+=+10%2F6+
+R%5Ba%5D%2FR%5Bc%5D+=+%281%2F220%29+%2F+R%5Bc%5D+
+10%2F6+=+%281%2F220%29+%2F+R%5Bc%5D+
+R%5Bc%5D+=+%286%2F10%29%2A%281%2F220%29+
+R%5Bc%5D+=+3%2F1100+
The rate for 40 adults is +40%2AR%5Ba%5D+=+40%2F220+
The rate for 80 children is +80%2AR%5Bc%5D+=+240%2F1100+
---------------------
Add the rates to get their rate working together
+40%2F220+%2B+240%2F1100+=+1%2Fd+ (1 tower in d days)
+2%2F11+%2B+12%2F55+=+1%2Fd+
Multiply both sides by 55d
+10d+%2B+12d+=+55+
+22d+=+55+
+2d+=+5+
+d+=+2.5+
It will take 50 adults and 80 children 2.5 days to build a tower

Answer by Edwin McCravy(20060) About Me  (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