Final answer:
Stephanie's rowing speed in still water is calculated using the difference in times rowing downstream and upstream on a river with a known current speed. By setting up an equation using the distances and speeds, and solving for her still water rowing speed, we find that it is 15 mph.
Step-by-step explanation:
The question asks for the rate at which Stephanie rows in still water, given her times rowing downstream and upstream on a river and the speed of the current. Let's assume Stephanie's rowing speed in still water is x mph. When she rows downstream, the river's current aids her, so her effective speed is x + 3 mph. Upstream, the current works against her, making her effective speed x - 3 mph. The distance of the trip is 182 miles each way.
Her time downstream is 182 / (x + 3) hours, and her time upstream is 182 / (x - 3) hours. We are given that the upstream journey takes 12 hours longer than the downstream journey, so we can set up the following equation:
182 / (x - 3) - 182 / (x + 3) = 12
Solving for x will give us Stephanie's rowing speed in still water. After finding a common denominator and simplifying, the equation becomes:
(182x + 546) - (182x - 546) = 12x2 - 36
This simplifies to:
12x2 - 182x - 36 = 0
Dividing through by 12, we get a quadratic equation in standard form, which we can solve using the quadratic formula, factoring, or graphing.
Upon solving the quadratic equation, we find that x = 15 mph (since a rowing speed of x must be a positive real number, we discard any negative solution).
Therefore, Stephanie's rowing speed in still water is 15 mph, which corresponds to option (c).