SOLUTION: If A works alone, he would take 4 days more to complete the job than if both A and B worked together. If B worked alone, he would take 16 days more to complete the job than if

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If A works alone, he would take 4 days more to complete the job than if both A and B worked together. If B worked alone, he would take 16 days more to complete the job than if       Log On


   



Question 850108: If A works alone, he would take 4 days
more to complete the job than if both A
and B worked together. If B worked alone,
he would take 16 days more to complete
the job than if A and B work together.
How many days would they take to
complete the work if both of them worked
together?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in days for A and B
to complete the work working together
------------------------
A and B rate working together:
( 1 job ) / t
A's rate working alone:
( 1 job ) / ( t + 4 )
B's rate working alone:
( 1 job ) / ( t + 16 )
-------------------
Add their rates to get their rate
working together
+1%2F%28+t+%2B+4+%29+%2B+1%2F%28+t+%2B+16+%29+=+1%2Ft+
Multiply both sides by +t%2A%28+t%2B4+%29%2A%28+t%2B16+%29+
+t%2A%28+t%2B16+%29+%2B+t%2A%28+t%2B4+%29+=+%28+t%2B4+%29%2A%28+t%2B16+%29+
+t%5E2+%2B+16t+%2B+t%5E2+%2B+4t+=+t%5E2+%2B+4t+%2B+16t+%2B+64+
+t%5E2+=+64+
+t+=+8+
It will take them 8 days to complete the work
if they work together
--------------------
check:
+1%2F%28+t+%2B+4+%29+%2B+1%2F%28+t+%2B+16+%29+=+1%2Ft+
+1%2F%28+8+%2B+4+%29+%2B+1%2F%28+8+%2B+16+%29+=+1%2F8+
+1%2F12+%2B+1%2F24+=+1%2F8+
+2%2F24+%2B+1%2F24+=+3%2F24+
OK