SOLUTION: sasha and matt are painting the apartments in a building in the summer. sasha was painting the apartments by herself for 9 days. after those 9 days, matt joined sahsha to help with

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Question 1021502: sasha and matt are painting the apartments in a building in the summer. sasha was painting the apartments by herself for 9 days. after those 9 days, matt joined sahsha to help with the painting. working together, they finished the apartments in 4 more days, meat could have painted all the apartments by himself in 22 days. how many days would it have taken sahsha to paint all the apartments alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call painting all the apartments 1 job
Let Sasha's rate of working alone = [ 1 job ] / [ t days ]
In 9 days she gets the following fraction of the job done:
+9%2Ft+
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The is +1+-+9%2Ft+ of the job left to do
------------
Working together with Matt, their rate of working was:
+%281+-+9%2Ft+%29%2F4+
---------------
Matt's rate of working alone is:
[ 1 job ] / [ 22 days ] = +1%2F22+
----------------------------
Add their rates of working to get their rate working together
+1%2Ft+%2B+1%2F22+=+%28%28+1+-+9%2Ft+%29%29+%2F+4+
Multiply both sides by +4%2A22t+
+4%2A22+%2B+4t+=+22t%2A%28+1+-+9%2Ft+%29+
+88+%2B+4t+=+22t+-+198+
+18t+=+286+
+t+=+15.889+
All alone, it would take her 15.889 days
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check:
+1%2Ft+%2B+1%2F22+=+%28%28+1+-+9%2Ft+%29%29+%2F+4+
+1%2F15.889+%2B+1%2F22+=+%28+1+-+9%2F15.889+%29+%2F+4+
+.0629+%2B+.0455+=+%28+1+-+.5664+%29+%2F+4+
+.1084+=+.4336%2F4+
+.1084+=+.1084+
OK
Hope I got it -the numbers are a little strange