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

you want the quick answer?

flvskidd · Answer

i think my teacher would want an explanation

anonymous · Answer

Good answer kid.

anonymous · Answer

using only the numbers given, 12 and 4, it will take them $$\frac{12\times 4}{12+4}$$ hours to do it
if you really want to impress your teacher, show where this easy answer comes from

anonymous · Answer

it is the reciprocal of what you get when you add the fraction 
one has rate $\frac{1}{12}$ the other has rate $\frac{1}{4}$
their combined rates is what you get when you add them, namely 
 $$\frac{1}{12}+\frac{1}{4}=\frac{12+4}{12\times 4}$$

anonymous · Answer

you then want to see how long it takes to complete ONE job (this is usually the confusing part) , in other words solve $$\frac{12+4}{12\times 4}T=1$$ for $T$ 
btw you can compute that number at any stime

anonymous · Answer

solve for $T$ via $$T=\frac{12\times 4}{12+4}$$

flvskidd · Answer

T = 48/16

anonymous · Answer

reduce to make it look nicer