SOLUTION: if sally can paint a room in 6 hours while it takes steve 7 hours to paint the same room. how long would it take them to paint the room if they worked together?

There are two ways to do it, one with algebra and one way without algebra. 
I'll show both ways.

WITHOUT algebra:

The least common multiple of 6 hours and 7 hours is 42 hours.  So in a 42 hour
period working together, Sally could paint 7 rooms while Steve paints 6.  So
together they would have painted 13 rooms in 42 hours, so together they could
paint 1 room in  hours or  hours. 

WITH algebra:

Sally can paint 1 room in 6 hours, so

Sally's painting rate is , or



Steve can paint a room in 7 hours, so

Steve's painting rate is .

or 
 
Let x = the number of hours it would take them to paint the room.

Their combined painting rate is .

or 

The equation comes from:





Multiply through by LCD 42x









Edwin