SOLUTION: Laundry can be completed in 3 hours if Fyona and Emmanuelle work together. How long will it take Fyona and Emmanuelle washing seperately if Fyona can do the task in half the time i

Question 1198432: Laundry can be completed in 3 hours if Fyona and Emmanuelle work together. How long will it take Fyona and Emmanuelle washing seperately if Fyona can do the task in half the time it would take Emmanuelle washing alone?
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Laundry can be completed in 3 hours if Fyona and Emmanuelle work together.
How long will it take Fyona and Emmanuelle washing separately if Fyona can do the task in half the time it would take Emmanuelle washing alone?
:
Let t = time required by F to do the job alone
"Fyona can do the task in half the time it would take Emmanuelle washing alone?
therefore
2t = time required by E to do the job
:
Write a shared work equation, each will do a fraction of the job.
The two fractions add up to 1

multiply equation by 2t, cancel the denominators
2(3) + 3 = 2t
6 + 3 = 2t
2t = 9
t = 9/2
t = 4.5 hrs, F working alone
then obviously,
2(4.5) = 9 hrs E working alone
:
You can substitute these two values in the shared work equation to cofirm this
:
Answer by greenestamps(13206) (Show Source): You can put this solution on YOUR website!

Fyona can do the task in half the time that Emmanuelle takes.

That means Fyona works twice as fast as Emmanuelle.

So when taking 3 hours to do the task together, Fyona does 2/3 of the task and Emmanuelle does 1/3.

Each working alone....

Emmanuelle: 1/3 of the task in 3 hours, so 9 hours to do the whole task alone.
Fyona: half the time Emmanuelle takes, so 9/2 = 4.5 hours.

ANSWERS: Emmanuelle 9 hours; Fyona 4.5 hours

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