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The correct answer is 3.43 hours.
To solve this problem, we need to calculate the combined work rate of Rosanne and Dorothy. Rosanne's work rate is 1/6 and Dorothy's work rate is 1/8.
When working together, their combined work rate is 1/6 + 1/8 = 7/24.
To find the number of hours it will take for them to bake the cookies together, we use the formula:
1 / ((1/6) + (1/8)) = 1 / (7/24) = 24/7 = 3.43 hours.
Therefore, it will take them approximately 3.43 hours to bake the cookies together.