SOLUTION: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together. I know that Sally can pa

Algebra ->  Equations -> SOLUTION: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together. I know that Sally can pa      Log On


   



Question 118453: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together.
I know that Sally can paint a house 2/3 faster than John.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together.
:
Let t = time required when painting together
:
Let the completed job = 1
:
A simple equation:
t%2F4 + t%2F6 = 1
;
Multiply equation by 12 to get rid of the denominators:
12*t%2F4 + 12*t%2F6 = 12(1)
:
Cancel out the denominators and you have:
3t + 2t = 12
:
5t = 12
:
t = 12/5
:
t = 2.4 hrs working together (and not fooling around)
:
:
Check our solution in the original equation:
2.4%2F4 + 2.4%2F6 =
.6 + .4 = 1, confirms out solution