SOLUTION: Angela takes 40 minutes to dust and clean her home while her sister rani takes an hour (6o min) to do same work. One day their mother joins the two sisters and together the three

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Question 480874: Angela takes 40 minutes to dust and clean her home while her sister rani takes an hour (6o min) to do same work. One day their mother joins the two sisters and together the three of them dust and clean their house in just 15 min. How long would their mother take if she did the job alone.
Answer by nerdybill(7384) About Me  (Show Source):
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Angela takes 40 minutes to dust and clean her home while her sister rani takes an hour (6o min) to do same work. One day their mother joins the two sisters and together the three of them dust and clean their house in just 15 min. How long would their mother take if she did the job alone.
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Let x = time (min) for mother to do it alone
then
15(1/40 + 1/60 + 1/x) = 1
multiplying both sides by 2400x:
15(60x + 40x + 2400) = 2400x
15(100x + 2400) = 2400x
1500x + 36000 = 2400x
36000 = 900x
40 mins = x