mrclassact2005 wrote:If Art and Rita can do a job in 4 hours when working together at their respective constant rates and Art can do the job alone in 6 hours, in how many hours can Rita do the job alone?
Let the job = 12 units.
Since the time for Art and Rita is 12 hours, their combined rate = w/t = 12/4 = 3 units per hour.
Since the time for Art alone is 6 hours, Art's rate alone = w/t = 12/6 = 2 units per hour.
Thus, Rita's rate alone = (Art and Rita's combined rate) - (Art's rate alone) = 3-2 = 1 unit per hour.
Thus, the time for Rita alone = w/r = 12/1 = 12 hours.
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