SOLUTION: Solve the problem. An experienced bank auditor can check a bank's deposits twice as fast as a new auditor. Working together it takes the auditors 4 hours to do the job. How long

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Solve the problem. An experienced bank auditor can check a bank's deposits twice as fast as a new auditor. Working together it takes the auditors 4 hours to do the job. How long      Log On


   

Question 824343: Solve the problem.
An experienced bank auditor can check a bank's deposits twice as fast as a new auditor. Working together it takes the auditors 4 hours to do the job. How long would it take the experienced auditor working alone?
Found 2 solutions by milo1954, josmiceli:
Answer by milo1954(10) About Me  (Show Source):
You can put this solution on YOUR website!
inexperience auditor takes 2X time
experience auditor takes X time
together = 4 hrs
2X+X=4
3X=4
X=4/3
X=1.33hrs

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the time in hours for the new auditor
to check a bank's deposits
An experienced bank auditor can check a bank's
deposits in +t%2F2+ hours
--------------------------
( 1 job / t hrs ) = the new auditor's rate of working
( 1 job / t/2 hrs ) = experienced auditor's rate of working
( 1 job / 4 hrs ) = their rate working together
------------------
Add their individual rates to get their rate working together
+1%2Ft+%2B+1%2F%28%28t%2F2%29%29+=+1%2F4+
+1%2Ft+%2B+2%2Ft+=+1%2F4+
Multiply both sides by +4t+
+4+%2B+8+=+t+
+t+=+12+ hrs
-------------
The experienced auditor's rate is:
+2%2Ft+=+2%2F12+
+2%2Ft+=+1%2F6+
The experienced auditor's rate is ( 1 job ) / ( 6 hrs ),
so it takes 6 hrs to check the bank