It takes Sally 6 hours longer than Joan to paint a room. Working together, they can paint the room in 4 hours. How long would it take each person working individually to paint the room?

Question

saifoo.khan · Answer

joan = x

Sally = x+ 6

$$\frac{1}{x} + \frac{1}{x+6} = \frac14$$Solve.:)

anonymous · Answer

Thanks, so then I get a common denomintor of 24?

saifoo.khan · Answer

nope,
$$\frac{1(x+6) + 1(x)}{x(x+6)} = \frac14$$

anonymous · Answer

wow I was really off :(  All this Algebra jargon is soooooo confusing.  Would you mind walking me through the rest of the problem?

saifoo.khan · Answer

Sure,
$$\frac{x+6 + x}{x^2 + 6x } = \frac14$$
$${4(2x+6)}={x^2 + 6x}$$

anonymous · Answer

ok, so you clear the fraction  by multiplying both sides by 4 right?  How did you get the bottom equation to the right of the equal sign?  I am sorry I am terrible at math and I am confused ;(

amistre64 · Answer

whatever we do to one side has to balance out on the other side.

multiply both sides be 4 (x^2+6x)  andsimplify

anonymous · Answer

ok thanks for your help! the whole problem is still very confusing to me.