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

anonymous · Answer

The sum of their rates is the combined rate. But we don't know the combined time. We'll solve for it.
$$\frac{ 1 }{ 12 }+\frac{ 1 }{ 4 } = \frac{ 1 }{ t }$$

In this case the LCM of the entire equation is 3*4*t, or 12t. Multiply everything by 12t.

$$t + 3t = 12$$
$$4t = 12$$
$$t = 3$$

So she is correct.

wolf1728 · Answer

Max can clean 1/12 house in 1 hour
Maggie can clean 1/4 house in an hour
If they work together, they can clean 1/12 plus 3/12 (4/12 or 1/3) of the house in 1 hour.
So, if they both work together it will take 3 hours.  
The sister is correct.