SOLUTION: Hello! I need help solving this...It takes Marcy�s apprentice 9 h longer to build a deck than it takes Marcy, an experienced carpenter. When they work together, they can build the

Question 728391: Hello! I need help solving this...It takes Marcy�s apprentice 9 h longer to build a deck than it takes Marcy, an experienced carpenter. When they work together, they can build the deck in 20h. How long would it take each person to build the deck working alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
It takes Marcy�s apprentice 9 h longer to build a deck than it takes Marcy, an experienced carpenter.
When they work together, they can build the deck in 20h.
How long would it take each person to build the deck working alone?
:
let m = M's time to build the deck alone
then
(m+9) = Apprentice time to do the job
:
Let the completed job = 1
:
Each will do a fraction of the job, the two fractions add up to 1.
:
A typical shared work equation
:
+ = 1
multiply by m(m+9), cancel the denominators, resulting in:
20(m+9) + 20m = m(m+9)
20m + 180 + 20m = m^2 + 9m
Combine like terms on the right side
0 = m^2 + 9m - 40m - 180
A quadratic equation
m^2 - 31m - 180 = 0
You can use the quadratic formula here, but this will factor to
(m-36)(m+5) = 0
The positive solution
m = 36 hrs M, working alone
then
36 + 9 = 45 hrs the apprentice working alone
:
:
See if that adds up using a calc
+ = 1
.56 + .44 = 1
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