Question

Brittany and Ashley can paint a room in 7 hours if they work together. If Ashley were to work by himself, it would take him 2 hours longer than it would take Brittany working by himself. How long would it take Brittany to paint the room by himself if Ashley calls in sick? Round to 2 decimal places.

Answer 1

Answer:

Step-by-step explanation:

Brittany paints the room in x hours, completing 1/x of the room per hour.

Ashley paints the room in x+2 hours, completing 1/(x+2) of the room per hour.

Working together, they complete 1/x + 1/(x+2) = ⅐ of the room per hour.

7(x+2) + 7x = x(x+2)

14x + 15 = x^2 + 2x

x^2 - 12x - 15 = 0

x = [12 ±√(12²+60)]/2= 6±√51

6-√51 is an extraneous solution.

x = 6+√51 ≈ 13.14

Brittany paints the room in 12.14 hours