SOLUTION: 5. Mary can clean an office complex in 5 hours.Working together John and Mary can clean the office complex in 3.5 hours.How long would it take John to clean the office complex by h

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 5. Mary can clean an office complex in 5 hours.Working together John and Mary can clean the office complex in 3.5 hours.How long would it take John to clean the office complex by h      Log On


   

Question 263015: 5. Mary can clean an office complex in 5 hours.Working together John and Mary can clean the office complex in 3.5 hours.How long would it take John to clean the office complex by himself?
6. Working alone,Maria can complete a task in 100 minutes.Nora can complete the same task in two hours.They work together for thirty minutes when Cita,the new employee,joins and begin helping.They finished the task 20 minutes later.How long would it take Cita to complete the task alone?

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Found 2 solutions by richwmiller, nerdybill:
Answer by richwmiller(17219) About Me  (Show Source):
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3.5/5+3.5/x=1
x=11 2/3 or 11 hrs 40 minutes

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
5. Mary can clean an office complex in 5 hours.Working together John and Mary can clean the office complex in 3.5 hours.How long would it take John to clean the office complex by himself?
.
Let x = time it would take for John to clean office alone
then
3.5(1/5 + 1/x) = 1
Multiplying both sides by 5x:
3.5(x + 5) = 5x
3.5x + 17.5 = 5x
17.5 = 1.5x
17.5/1.5 x
175/15 = x
35/3 = x
11 2/3 hours = x
or
11 hours and 40 minutes = x
.
6. Working alone,Maria can complete a task in 100 minutes.Nora can complete the same task in two hours.They work together for thirty minutes when Cita,the new employee,joins and begin helping.They finished the task 20 minutes later.How long would it take Cita to complete the task alone?
.
First, convert the 2 hours into minutes:
2*60 = 120 minutes
.
Let x = time it takes Cita to complete task alone
then
30(1/100 + 1/120) + 20(1/100 + 1/120 + 1/x) = 1
Multiplying both sides by (100)(120)x:
30(120x + 100x) + 20(120x + 100x + 12000) = 12000x
Divide both sides by 10:
3(120x + 100x) + 2(120x + 100x + 12000) = 1200x
360x + 300x + 240x + 200x + 24000 = 1200x
1100x + 24000 = 1200x
24000 = 100x
240 minutes = x
or
4 hours = x
So Cita can do the task alone in 4 hours.