SOLUTION: Vic and Alou together can do a certain job in 15 days. Vic starts working but quits after 10 days. Alou continues the job and finishes it in 18 days. How long would it take each to

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Vic and Alou together can do a certain job in 15 days. Vic starts working but quits after 10 days. Alou continues the job and finishes it in 18 days. How long would it take each to      Log On


   

Question 785763: Vic and Alou together can do a certain job in 15 days. Vic starts working but quits after 10 days. Alou continues the job and finishes it in 18 days. How long would it take each to do the job alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R%5Bv%5D+ = Vic's rate of working in ( jobs ) / ( days )
Let +R%5Ba%5D+ = Alou's rate of working in ( jobs ) / ( days )
( 1 job ) / ( 15 days ) = +1%2F15+
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(1) +R%5Bv%5D+%2B+R%5Ba%5D+=+1%2F15+
--------------------------
What fraction of the job does Vic get done in +10+ days?
He does +10R%5Bv%5D+ of the job
Then there is +1+-+10R%5Bv%5D+ of the job left to do
---------------------
Alou does this in +18+ days
(2) +R%5Ba%5D+=+%28+1+-+10R%5Bv%5D+%29+%2F+18+
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(1) +R%5Ba%5D+=+1%2F15+-+R%5Bv%5D+
Substitute (1) into (2)
(2) +1%2F15+-+R%5Bv%5D+=+%28+1+-+10R%5Bv%5D+%29+%2F+18+
Multiply both sides by +18+
(2) +18%2F15+-+18R%5Bv%5D+=+1+-+10R%5Bv%5D+
(2) +6%2F5+-+18R%5Bv%5D+=+1+-+10R%5Bv%5D+
Multiply both sides by +5+
(2) +6+-+90R%5Bv%5D+=+5+-+50R%5Bv%5D+
(2) +40R%5Bv%5D+=+1+
(2) +R%5Bv%5D+=+1%2F40+
------------------------
And, since
(1) +R%5Bv%5D+%2B+R%5Ba%5D+=+1%2F15+
(1) +1%2F40+%2B+R%5Ba%5D+=+1%2F15+
Multiply both sides by +40%2A15+
(1) +15+%2B+40%2A15%2AR%5Ba%5D+=+40+
(1) +40%2A15%2AR%5Ba%5D+=+25+
(1) +8%2A15%2AR%5Ba%5D+=+5+
(1) +8%2A3%2AR%5Ba%5D+=+1+
(1) +R%5Ba%5D+=+1%2F24+
-------------------------
Vic takes 40 days working alone
Alou takes 24 days working alone
--------------------------------
check:
(2) +R%5Ba%5D+=+%28+1+-+10R%5Bv%5D+%29+%2F+18+
(2) +1%2F24+=+%28+1+-+10%2F40+%29+%2F+18+
Multiply both sides by +24+
(2) +1+=+%2824%2F18%29%2A%28+3%2F4%29+
Multiply both sides by +18%2A4+
(2) +18%2A4+=+24%2A3+
(2) +72+=+72+
OK
(1) +R%5Bv%5D+%2B+R%5Ba%5D+=+1%2F15+
(1) +1%2F40+%2B+1%2F24+=+1%2F15+
(1) +24%2A15+%2B+40%2A15+=+24%2A40+
(1) +15%2A%28+24+%2B+40+%29+=+960+
(1) +15%2A64+=++960+
(1) +960+=+960+
OK