SOLUTION: Pam and Matt, working together, can weed the garden in 8 hours. Working alone, Matt takes twice as long as Pam. How long does it take Pam to weed the garden alone?

Question 1157868: Pam and Matt, working together, can weed the garden in 8 hours. Working alone, Matt takes twice as long as Pam. How long does it take Pam to weed the garden alone?

Found 3 solutions by mananth, MathTherapy, greenestamps:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

Pam and Matt, working together, can weed the garden in 8 hours. Working alone, Matt takes twice as long as Pam. How long does it take Pam to weed the garden alone?
let Pam take x hours to weed the garden
Pam does 1/x of the job in 1 hour
Matt takes 2x hours
Matt does 1/2x of the job in 1 hour
Together they take 8 hours
Together they do 1/8 of the job in 1 hour
1/x + 1/2x = 1/8
(2+1)/2x =1/8
3/2x = 1/8
2x=24
x= 12
Pam takes 12 hours

Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Pam and Matt, working together, can weed the garden in 8 hours. Working alone, Matt takes twice as long as Pam. How long does it take Pam to weed the garden alone?

Let time Pam takes be P
Then time Matt takes is 2P
We then get:
8 + 4 = P ------ Multiplying by LCD, 8P
Time Pam takes, or
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

An alternative solution method....

Working alone, Matt takes twice as long as Pam. [given]
When they work together, Pam does 2/3 of the job. [logical reasoning]
So Pam does 2/3 of the job in 8 hours; that means working alone it will take her 8(3/2)=12 hours to do the whole job.

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