Question

working together Rick and Juanita can complete a job in 6 hours. it would take rick 9 hours longet then juanita to do the job alone. how long would it take juanita?

Answer 1

Rick can do 1/R of the job in one hour. Juanita can do 1/J of the job in one hour.

Together, they can do 1/6 of the job in an hour.

Therefore, 1/J + 1/R = 1/6

Rick can do the job alone in R hours, which is 9 hours more than the J hours Juanita would take.
R = J + 9
1/J + 1/(J + 9) = 1/6
6(J + 9) + 6J = J² + 9J
J² - 3J - 54 = 0
(J - 9)(J + 6) = 0
J = 9 hours

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