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?

Algebra ->  Rate-of-work-word-problems -> 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?       Log On


   



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) About Me  (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) About Me  (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: matrix%281%2C3%2C+1%2FP+%2B+1%2F%282P%29%2C+%22=%22%2C+1%2F8%29
8 + 4 = P ------ Multiplying by LCD, 8P
Time Pam takes, or highlight_green%28matrix%281%2C4%2C+P%2C+%22=%22%2C+12%2C+hours%29%29

Answer by greenestamps(13198) About Me  (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.