SOLUTION: Ralph paints a room in k hours, Jenny paints the room in m hours. Jenny takes two more hours to paint than Ralph. Together they can paint in 8 hours. How many hours can each pai

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Ralph paints a room in k hours, Jenny paints the room in m hours. Jenny takes two more hours to paint than Ralph. Together they can paint in 8 hours. How many hours can each pai      Log On


   

Question 1089967: Ralph paints a room in k hours, Jenny paints the room in m hours. Jenny takes two more hours to paint than Ralph. Together they can paint in 8 hours. How many hours can each paint the room on their own.
Found 3 solutions by jhunjiro, MathTherapy, Fombitz:
Answer by jhunjiro(67) About Me  (Show Source):
Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Ralph paints a room in k hours, Jenny paints the room in m hours. Jenny takes two more hours to paint than Ralph. Together they can paint in 8 hours. How many hours can each paint the room on their own. 
Correct answer: By themselves,

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate x Time = Output
.
.
.
Let's say that an output of 100 is required for the room to be painted (this number is arbitrary).
R%5BR%5D%2Ak=100
R%5BR%5D=100%2Fk
.
.
R%5BJ%5D%2Am=100
R%5BJ%5D=100%2Fm
and
m=k%2B2
and
%28R%5BR%5D%2BR%5BJ%5D%298=100
R%5BR%5D%2BR%5BJ%5D=25%2F2
100%2Fk%2B100%2Fm=25%2F2
8%2Fk%2B8%2Fm=1
8%2Fk%2B8%2F%28k%2B2%29=1
8k%2B8%28k%2B2%29=k%28k%2B2%29
8k%2B8k%2B16=k%5E2%2B2k
k%5E2-14k-16=0
Completing the square,
%28k%5E2-14k%2B49%29-16=49
%28k-7%29%5E2=65
k-7=0+%2B-+sqrt%2865%29
k=7+%2B-+sqrt%2865%29
Only positive values of k are acceptable for this problem.
So then,
R%5BR%5D=7%2Bsqrt%2865%29
R%5BJ%5D=7%2Bsqrt%2865%29%2B2=9%2Bsqrt%2865%29