I just worked out a problem that gave me and answer of 1 but when checked with the correct answer it was 1.2......Here is the problem

Erin can paint a room in 3hrs and her hubby can do it in 2hrs, how long will it take both to paint the room together?! (simplified the question)

Ok! so knowing that

Erin=3x and Hubby=2x the problem then is written like this....(right?)

1x over 3 plus 1x over 2 equals 1

+

1x1x= 1

3.....2

ok now the LCD is 6 and then multiply all by (6)

(6)1x+ (6)1x= 1(6)

3..........2

cancel the 6 and the 3 = 2 and the 6 and the 2 = 3 right!?

so now we have

2x + 3x = 6 combine like terms;

6x = 6

and then solve for $\displaystyle x$

x=1

so far so good or did I dushbag it somewhere?!