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Noah's contracting company builds road at a rate of 1 mile per week, except during the rainy season, when that rate drops to $$\frac{1}{2}$$ mile per week. If Noah is hired to build 11 miles of road, and his company begins construction 5 weeks before the start of the rainy season, how many weeks will it take Noah's company to complete the contract? (Rainy season lasts 14 weeks.)_____

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