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?

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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) About Me  (Show Source):
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Andrea's rate 1%2Fx
Samantha's rate, 1%2F2x
-
1%2Fx%2B1%2F%282x%29=1%2F6
Simplify and solve.

6x%281%2Fx%2B1%2F%282x%29%29=6x%281%2F6%29
6%2B3=x
highlight%28x=9%29-------------hours for Andrea to do the job alone

Answer by greenestamps(13200) About Me  (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.