SOLUTION: it takes mary 3 hours more to do a job than it takes jane. if they work together,they can finish the same job in 2 hours. how long would it take mary to finish the job alone?

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Question 983856: it takes mary 3 hours more to do a job than it takes jane. if they work together,they can finish the same job in 2 hours. how long would it take mary to finish the job alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working to get
their rate working together
------------------------
Let +1%2Ft+ = Jane's rate of working
expressed as [ 1 job ] / [ t hrs ]
---------------------------
Mary's rate is:
+1%2F%28+t%2B3+%29+ = { 1 job ] / [ t + 3 hrs ]
-----------------------------------
Their rate working together is:
+1%2F2+ = [ 1 job ] / [ 2 hrs ]
---------------------------
+1%2Ft+%2B+1%2F%28+t%2B3+%29+=+1%2F2+
Multiply both sides by +2t%2A%28+t%2B3+%29+
+2%2A%28+t%2B3+%29+%2B+2t+=+t%2A%28+t%2B3+%29+
+2t+%2B+6+%2B+2t+=+t%5E2+%2B+3t+
+t%5E2+-+t+-+6+=+0+
By looking at this, I see the solution is:
+%28+t+-+3+%29%2A%28+t+%2B+2+%29+=+0+
Time can't be negative, so the solution is:
+t+=+3+ hrs
and
+t+%2B+3+=+6+ hrs
It takes Mary 6 hrs to finish the job alone
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check answer:
+1%2Ft+%2B+1%2F%28+t%2B3+%29+=+1%2F2+
+1%2F3+%2B+1%2F%28+3%2B3+%29+=+1%2F2+
+2%2F6+%2B+1%2F6+=+1%2F2+
+3%2F6+=+3%2F6+
OK