College Algebra word problem?
Betty and Karen have been hired to paint the houses in a new development. Working together, the women can paint a house in two-thirds the time that it takes Karen working alone. Betty takes 6h to paint a house alone. How long does it take Karen to paint a house working alone?
Comments
Betty can paint 1/6 of a house in an hour. Karen takes H hours to paint a house, so can paint 1/H of a house in one hour.
In one hour, the two of them can paint 1/6 plus 1/H of the house
M3 was right that I messed up. But he's still wrong about his notions about how to simplify the problem. Looks like here was where I made my big mistake.
1/6 + 1/H = 2/3 times H
The expression on the left-hand side should have been the inverxe of what I wrote, making the equation look like this:
1/(1/6 + 1/H) = (2/3)H, which becomes:
1/((H+6)/6h) = 2H/3, which becomes:
6H / (H+6) = 2H/3
Cross-multiplying gives you
18H = 2H^2 + 12H, or
2H^2 - 6H = 0
H^2 - 3H = 0
So H = 0 or H-3 = 0
So H = 3