Max and Maggie have to clean the house. It takes Max 12 hours to clean the house, while Maggie can complete the task in 4 hours. Their sister says that it will take 3 hours to complete if they work together. Explain each step in solving this equation, and determine if the sister is correct or not.

Question

mathmate · Answer

The trick is to find out how much (in fraction) of the work each can accomplish in one hour.
Max can finish 1/12 of the job in one hour.
Maggie can do 1/4 of the job in one hour.
If they work together, the can accomplish (1/12+1/4)=(1/12+3/12)=(1+3)/12=1/3 of the job in one hour.
To do the whole job, it will take them 1/(1/3)=3 hours.
So Maggie was right!
She's amazing, not only works fast, but also calculates fast!  lol

monteskellie · Answer

Thank you