Michelle can complete a landscaping job in 6 days and Danielle can complete the same job in 4 days. Working together, in how many days could they complete the job?

The correct answer is: 2 2/5 days

Let’s say the total work done is W and let’s say the work done by Michelle in one day is W_M and work done by Danielle in one day is W_D
Step 1 of 3:
It is given that Michelle completes the job in 6 days. So we can write
W_M × 6 = W
W_M =   …….(1)
It is given that Danielle completes the job in 4 days. So we can write
W_D × 4 = W
W_D =   …….(2)
Step 2 of 3:
Now, adding equations (1) and (2)
W_M + W_D=  +  
W_M + W_D =    ……(3)
Step 3 of 3:
From equation (3), we get to know that  work is done by both of them in one day.
So, the number of days required by all three to complete W work =   =   =  days
Final Answer:
Hence, if they worked together it would take  days.