SOLUTION: Andrea takes half the time it takes Samantha to do a certain job, if they work together they will take 6 hours. How long will Andrea to do it alone?

Question 1134009: Andrea takes half the time it takes Samantha to do a certain job, if they work together they will take 6 hours. How long will Andrea to do it alone?
Found 3 solutions by Glaviolette, josgarithmetic, greenestamps:
Answer by Glaviolette(140)   (Show Source): You can put this solution on YOUR website!

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Andrea's rate
Samantha's rate,
-

Simplify and solve.

-------------hours for Andrea to do the job alone
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Obviously one of the answers you have received makes no sense; it can't take them 2 hours and 4 hours individually if it takes them 6 hours together.

Here is a different way than shown by the other tutor to get the correct answer of 9 hours for the time it takes Andrea to do the job alone.

(1) It takes Andrea half as long as Samantha to do the job; that means she works twice as fast as Samantha.

(2) When working together, the two of them take 6 hours to do the job; and, since Andrea works twice as fast as Samantha, she does 2/3 of the job.

(3) Then since Samantha does 2/3 of the job in 6 hours, she can do the whole job herself in (3/2) times 6 hours, or 9 hours.
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