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Jane needs 3 hours to clean the Smith house. Her younger sister, Alice, can clean the house in 5 hours. How long would the sisters, working together, need to clean the house?

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Final answer:

Together, Jane and Alice can clean the house in 1 hour and 52.5 minutes since their combined rate of cleaning is 8/15 of the house per hour.

Step-by-step explanation:

Jane and Alice are working together to clean a house and we need to determine how long it will take them. To calculate their combined rate of work, we can add their individual rates. Jane cleans the house in 3 hours, so her rate is 1/3 of the house per hour. Alice cleans the house in 5 hours, which means her rate is 1/5 of the house per hour. Working together, their combined rate is 1/3 + 1/5 = 5/15 + 3/15 = 8/15 of the house per hour. To find out how long it takes to clean the whole house together, we calculate the reciprocal of their combined rate: 15/8 hours, which is 1 hour and 52.5 minutes.

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