SOLUTION: Amy can clean the house in 9 hours. When she works together with Tom, the job takes 5 hours. How long would it take Tom, working by himself, to clean the house?

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Question 709181: Amy can clean the house in 9 hours. When she works together with Tom, the job takes 5 hours. How long would it take Tom, working by himself, to clean the house?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Same job, each worker different rates.
R%5Ba%5D Amys' rate
R%5Bt%5D Toms' rate (Our unknown variable to find)
R%5Bs%5D Sum of their rates working together

R%5Ba%5D%2BR%5Bt%5D=R%5Bs%5D
From given,
1%2F9%2BR%5Bt%5D=1%2F5
R%5Bt%5D=1%2F5-1%2F9
R%5Bt%5D=%289-5%29%2F45
highlight%28R%5Bt%5D=4%2F45%29, as jobs per hour.

If you want as how many HOURS per JOB, then use reciprocal.
highlight%2845%2F4=11%261%2F4%29, hours per job.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of working to get rate
working together
Amy's rate is ( 1 house ) / ( 9 hrs )
Let +1%2Ft+ = Tom's rate
Their rate working together is +1%2F5+
-------------------------------------------
given:
+1%2F9+%2B+1%2Ft+=+1%2F5+
Multiply both sides by +45t+
+5t+%2B+45+=+9t+
+4t+=+45+
+t+=+13.75+
It will take Tom 13 hrs and 45 min working alone
check:
+1%2F9+%2B+1%2Ft+=+1%2F5+
+1%2F9+%2B+1%2F13.5+=+1%2F5+
You can check with calculator