SOLUTION: Suppose Marco can stuff envelopes twice as fast as his friend Polo. Together, they can stuff 6750 envelopes in 4.5 hours. How long would it take each of them working alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Suppose Marco can stuff envelopes twice as fast as his friend Polo. Together, they can stuff 6750 envelopes in 4.5 hours. How long would it take each of them working alone?      Log On


   

Question 735886: Suppose Marco can stuff envelopes twice as fast as his friend Polo. Together, they can stuff 6750 envelopes in 4.5 hours. How long would it take each of them working alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working alone to get
their rates working together
For this problem call stuffing 6750 envelopes
1 job.
Let +t+ = Polo's time in hours to do 1 job
+2t+ = Marco's time in hrs to do 1 job
------------------------------------
( 1 job / t hrs ) + ( 1 job / 2t hrs ) = 1 job / 4.5 hrs
+1%2Ft+%2B+1%2F%282t%29+=+1%2F4.5+
Multiply both sides by +9t+
+9+%2B+4.5+=+2t+
+2t+=+13.5+
+t+=+6.75+
+2t+=+13.5+
Marco does the job in 13.5 hrs
Polo does the job in 6.75 hrs
check:
+1%2Ft+%2B+1%2F%282t%29+=+1%2F4.5+
+1%2F6.75+%2B+1%2F13.5+=+1%2F4.5+
+.148148+%2B+.074074+=+.222222+
+.222222+=+.222222+
OK