SOLUTION: Your friend can address envelopes twice as fast as you can. Together you and your friend address all the invitations envelopes in 3 hours. How long would it take your friend to add

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Your friend can address envelopes twice as fast as you can. Together you and your friend address all the invitations envelopes in 3 hours. How long would it take your friend to add      Log On


   

Question 634465: Your friend can address envelopes twice as fast as you can. Together you and your friend address all the invitations envelopes in 3 hours. How long would it take your friend to address the envelopes the alone.
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Your friend can address envelopes twice as fast as you can. Together you and your friend address all the invitations envelopes in 3 hours. How long would it take your friend to address the envelopes the alone.
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Your time = 2x hrs/job ; rate = 1/(2x) job/hr
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Friends time = x hrs/job ; rate = 1/x job/hr
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Together time = 3 hrs/job ; rate = 1/3 job/hr
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Equations:
rate + rate = together rate
1/(2x) + 1/x = 1/3
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Multiply thru by 6x to get:
3 + 6 = 2x
2x = 9
x = 4.5 hrs (friends's time to do the job)
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2x = 9 hrs (your time to do the job)
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +r+ = your rate of addressing all invites
+2r+ = your friend's rate
Add the rates to get the rate doing it together
+r+%2B+2r+=+1%2F3+
Note that 1/3 is ( all invites ) / ( 3 hrs )
+3r+=+1%2F3+
+r+=+1%2F9+
+2r+=+1%2F4.5+
Your friend takes 4 and a half days alone