i need help with this algebra word problem?

Question

an experienced bank auditor can check a bank's deposits twice as fast as a new auditor. Working together it takes the auditors 18 hrs. to do the job. How long would it take the experienced auditor working alone?

Answer 1

let t be the time it takes the experienced bank auditor to check a bank's deposits. Then in 1hr, he/she can check 1/t of the bank's deposits

Then 2t is the time it takes the new auditor to check a bank deposits. Then in 1hr, he/she can check 1/(2t) of the bank's deposite

Given that if they work together, they finish in 18hrs. That means how much of the bank deposit the experienced bank auditor can check in 18hrs PLUS how much of the bank deposit the new auditor can check in the SAME amount of time will equal to 100% of the bank deposits

18(1/t) + 18[ 1/(2t) ] = 100%
18/t + 18/(2t) = 1
36t + 18t = 2t^2
54t = 2t^2
2t^2 - 54t = 0
2t (t - 27)
t = 0 or 27

it takes some times to finish the job, so take 27 as the answer

So it takes the experienced bank auditor 27hrs to check bank's deposite and it takes the new auditor 54hrs to check bank's deposits.

hope it helps

Answer 2

18 + 9 = 27 hours
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Ideas for mental math approach: Since the experienced auditor can work twice as fast as a new auditor, and when they work together, it took the new auditor 18 hrs, the experienced auditor needs to spend 9 more hrs.

Answer 3

6

Answer 4

12?