Three bricklayers, Maric, Hugh and Ethan, are cladding a new home. If Maric were to work alone, the job would take him 8 days to complete. If Hugh were to work alone, the job would take him 6 days to complete and if Ethan were to work by himself, the job would take him 12 days to complete. a) If the three men work together, how long will it take them to complete the job? b) What fraction of the house will each bricklayer complete?

The correct answer is: a) 2 2/3 , b)2/9

Let’s say the work done to build the home is W and let’s say the work done by Maric in one day is W_M, work done by Hugh in one day is W_H and work done by Ethan in one day is W_E.
Step 1 of 2:
It is given that Maric builds the home in 8 days. So we can write
W_M × 8 = W
W_M =     …….(1)
It is given that Hugh builds the home in 6 days. So we can write
W_H × 6 = W
W_H =     …….(2)
It is given that Ethan builds the home in 12 days. So we can write
W_E  12 = W
W_E =   …….(3)

Step 2 of 2:
Now, adding equations (1), (2) and (3)
W_M + W_H + W_E =  +  + 
W_M + W_H + W_E =   ……(4)
a)
From equation (4), we get to know that  work is done by all three in one day.
So, the number of days required by all three to complete W work =  =  =  days
Final Answer:
Hence, it would take  days to build the house all the three men worked together.
b)
Work done by Maric in  days = W_M ×  =  × =  
Work done by Hugh in  days = W_H ×  =  ×  = 
Work done by Ethan in  days = W_E ×  =  ×  = 
Final Answer:
Hence, Maric will build of the house, Hugh will of the house and Ethan will build of the house.