Final answer:
To solve for Linda's rowing speed in still water, we use the information about her downstream and upstream trips considering the current's speed. By setting up and solving a system of equations involving her travel times and distances, we determine her speed in still water to be 15 mph.
Step-by-step explanation:
The question is asking us to determine the speed at which Linda rows in still water given that she rows downstream for 99 miles and the return trip upstream takes 24 hours longer, with the current flowing at 4 mph.
To solve this, we need to set up two equations, one for the downstream trip and one for the upstream trip. Let's let x be Linda's speed in still water. Downstream, her speed would be x + 4 mph (speed in still water plus the current) and upstream it would be x - 4 mph (speed in still water minus the current).
The time it takes to travel a certain distance is equal to the distance divided by the speed. For the downstream trip, the time t would be 99 miles divided by (x + 4) mph. For the upstream trip, the time would be 99 miles divided by (x - 4) mph, and this is also t + 24 hours longer than the downstream trip.
We can set up the following equations:
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- Downstream: t = 99 / (x + 4)
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- Upstream: t + 24 = 99 / (x - 4)
By solving the system of equations, we find out that Linda's speed in still water is 15 mph, which corresponds to option A.