Question

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. Explaining each step in solving this equation, and determine if the sister is correct or incorrect.

Answer 1

For Max, it takes 12 hours to clean the house, so in 1 hour he will complete 1/12 of the task.

For Maggie, it take 4 hours to clean the house, so in 1 hours she will complete 1/4 of the task.

Both of them working together means that in 1 hour they will complete 1/12 plus 1/4:

$\frac{1}{12}+\frac{1}{4}=\frac{1}{12}+\frac{3}{12}=\frac{4}{12}=\frac{1}{3}$

Thus, in 1 hours both working together will make 1/3 of the task. To make the full task, they will need a total of 3 hours, because:

$3\cdot\frac{1}{3}=1$

That is, 3 hours times the fraction of the task per hours gives 1 total task.

So, they will need 3 hours to complete and the sister is correct.