Lizzie can paint a fence in 6 hours, while it takes Alex 8 hours to paint the same fence. How long in hours would it take them to paint the fence if they worked together? Express your answer as a common fraction.
Lizzie's rate is 1 fence in 6 hours, or 1/6.
Alex's rate is 1 fence in 8 hours, or 1/8.
Since they work the same amount of time, time = t.
amount completed = rate x time
amount Lizzie does + amount Alex does = total amount completed
(1/6)(t) + (1/8)(t) = 1 fence painted
(7/24)(t) = 1
t = 1 / (7/24)
t = 24/7 hours