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In 1 minute mother can clean 1/45 of the house while daughter can clean 1/60 of the house.

Together they can clean 1/45+1/60=(4+3)/180=7/180 in one minute.

So they can clean the whole house together in 180/7=25⁵⁄₇ minutes, about 25m 43s.


In quarter of an hour mother can clean 1/3 of the house but daughter can only clean 1/4 of the house. Working together they can clean 1/3+1/4=7/12 of the house in quarter of an hour. So it would take 12/7 quarter hours to clean the whole house: 12/7×15 minutes=180/7 mins=25⁵⁄₇ mins. 

If the house has 12 rooms, mother can clean 4 rooms, but daughter only 3 in 15 minutes. So they can clean 7 rooms between them in 15 minutes. That means by proportion they can clean 12 rooms in 12/7×15=180/7 mins.

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