SOLUTION: Hi, can you help me understand this! "Tim can build 3 shelves in one day and Al can build 4 shelves in 2 days. If Al starts work one day before Tim, how long will they work toge

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Hi, can you help me understand this! "Tim can build 3 shelves in one day and Al can build 4 shelves in 2 days. If Al starts work one day before Tim, how long will they work toge      Log On


   



Question 450701: Hi, can you help me understand this!
"Tim can build 3 shelves in one day and Al can build 4 shelves in 2 days. If Al starts work one day before Tim, how long will they work together to build 22 shelves?"
Thank you very much for your time!

Found 2 solutions by Edwin McCravy, josmiceli:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, can you help me understand this!
"Tim can build 3 shelves in one day and Al can build 4 shelves in 2 days. If Al starts work one day before Tim, how long will they work together to build 22 shelves?"
Thank you very much for your time!

Al can build 4 shelves in 2 days, 
so Al can build 2 shelves in 1 day.

Tim can build 3 shelves in 1 day,

So Al and Tim together can build 
2+3 or 5 shelves in 1 day.

Since Al can build 2 shelves in 1 day, 
then in the first day when he works alone,
he will build 2 shelves.  That leaves
22-2 = 20 shelves left to build.

They will build the remaining 20 shelves 
working together.

Since Al and Tim together can build 
5 shelves in 1 day, and since 20÷5 = 4,

it will take then 4 days to build the remaining
20 shelves.

Edwin


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working to get their rate
working together.
Their rates are: (number of shelves built) / (days to build that many shelves)
-----------------
The question is: how many shelves does Al build in his 1 day head start?
+4%2F2++=+x%2F1+
+x+=+2+
Al builds 2 shelves, and then Tim joins him. Now they only have to
build 20 shelves.
Working together:
+3%2F1+%2B+4%2F2+=+20%2Fx+
Multiply both sides by 2x
6x+%2B+4x+=+40+
+10x+=+40+
+x+=+4+
Together they can build 20 shelves in 4 days.
+1+%2B+4+=+5+
They build 22 shelves in 5 days