SOLUTION: One custodian cleans a suite of offices in 2 hours. When a second worker is asked to join the regular​ custodian, the job takes only 1 and one third hours. How long does it t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: One custodian cleans a suite of offices in 2 hours. When a second worker is asked to join the regular​ custodian, the job takes only 1 and one third hours. How long does it t      Log On


   

Question 1080277: One custodian cleans a suite of offices in 2 hours. When a second worker is asked to join the regular​ custodian, the job takes only 1 and one third hours. How long does it take the second worker to do the same job​ alone?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
1st custodian's rate of working:
[ 1 office cleaned ] / [ 2 hrs ]
Their rate working together:
[ 1 office cleaned ] / [ 4/3 hrs ]
Let +t+ = the second worker's time
in hrs to clean the office
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Add their rates of working to get their
rate working together
+1%2F2+%2B+1%2Ft+=+1%2F%28%284%2F3%29%29+
+1%2F2+%2B+1%2Ft+=+3%2F4+
Multiply both sides by +4t+
+2t+%2B+4+=+3t+
+t+=+4+
The 2nd worker takes 4 hrs to do the job alone
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check:
+1%2F2+%2B+1%2Ft+=+3%2F4+
+1%2F2+%2B+1%2F4+=+3%2F4+
+2%2F4+%2B+1%2F4+=+3%2F4+
+3%2F4+=+3%2F4+
OK