P, Q, and R are three workers who can complete a certain job. P alone can finish the job in 12 days. Q alone can finish the same job in 3N days. Q and R together can complete the job in N days. P and Q start the work together and continue for 4 days, after which they leave. The remaining work is completed by R alone in 9 days. Find the value of N.

Using the work and time method, P's 1 day work is 1/12, Q's 1 day work is 1/(3N) and R's 1 day work is (1/N) - (1/(3N)) = 2/(3N). From the given execution scenario, the work done by P and Q in 4 days is 4 * (1/12 + 1/(3N)), and the work done by R in 9 days is 9 * (2/(3N)). The sum of these parts equals 1 whole job: 4/12 + 4/(3N) + 18/(3N) = 1. Simplifying this equation gives 1/3 + 22/(3N) = 1, which results in 3N = 33, so N = 11.

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