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Answer:
3 hours
Step-by-step explanation:
Max cleans the house in 12 hours
Max in 1 hour cleans: 1/12 part of the house
Maggie cleans the house in 4 hours
Maggie in 1 hour cleans: 1/4 part of the house
In 1 hour they together do: 1/12 + 1/4 = 1+3/12 = 4/12 = 1/3 work
1 hour===1/3 work
X hours== 1 work
X/3 = 1
X = 3 hours.
Hence, they together complete the work in 3 hours.
And so, the sister is correct.
Hope it helps.