how long will it take them to clean the house

Question

Liberty can clean the house in 4 hours. Her husband Darrell can do the same job in 6 hours. If the two work together, how long will it take them to clean the house

Answer 1

1house/4hrs + 1house/6hrs = 1house/xhrs

 

1/4 + 1/6 = 1/x

 

(1/4)*(6/6) + (1/6)*(4/4) = 1/x

 

6/24 + 4/24 = 1/x

 

10/24 = 1/x

 

cross multiply

 

10x = 24

 

x = 24/10 = 2.4 hrs