It takes Henry 8 hours longer to paint one room than it does Sally. If they work together Sally and Henry can paint one room in 3 hours. How long does it take

Question

Sally in hours, working alone, to paint one room?

Answer 1

Sally paints a room in x hours, so she paints 1/x of the room in 1 hour.

Henry paints a room in x+8 hours, so he paints 1/(x+8) of the room in 1 hour.

Together they paint the room in 3 hours, so they paint 1/3 of the room in an hour.

 

1/x + 1/(x+8) = 1/3

 

Multiply each term by the least common multiple of the denominators (3x² + 24x) to eliminate them.

 

3x + 24 + 3x = x² + 8x

x² + 2x - 24 = 0

(x + 6)(x - 4) = 0

x = -6, 4

 

Sally can't do it in negative time, so it takes her 4 hours by herself.