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

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) (Show Source): You can put this solution on YOUR website!
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.
.
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

RELATED QUESTIONS
A wife picks up her husband after work at a certain hour every day. (It takes the same... (answered by ankor@dixie-net.com)

if it takes my sister 2 hours to clean her room. and it takes me 1 hour and 30 minutes to (answered by jorel1380)

lisa can sweep the paths around her home in 30 minutes. Her sister Tania takes 20 minutes (answered by nerdybill)

It takes 45 min for a mother to clean her house. Her daughter can do the job in 1 hour.... (answered by josgarithmetic)

two siblings-a brother and sister-attend the same school. Walking at constant rates the... (answered by josmiceli)

Nancy takes an hour and a half to rake the lawn. But it takes her only 40 minutes if her... (answered by stanbon)

It takes Kathy 3 hours and 40 minutes to clean the kitchen of her house. Find her work... (answered by stanbon)

Sarah takes 40 minutes to walk to her office and only 12 min if she rides her bike. Her... (answered by ankor@dixie-net.com)

Judie can clean her room in 60 minutes if her sister can help her, it takes them 36... (answered by nyc_function)