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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.

 Jun 8, 2020
 #1
avatar+21953 
+1

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     

 Jun 8, 2020

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