QuestionA kayaker spends 2 hours paddling up a stream from point $A$ to point $B$, quickly turns her kayak around, and immediately heads back downstream. It takes her only 1 hour to float back down the stream from point $B$ to point $A$. If points $A$ and $B$ are 6 miles apart, what was the kayaker's average rate of speed in miles per hour? A. 12 mph B. 6 mph C. 4 mph D. 2 mph

Studdy Solution
To find the kayaker's average speed over the entire trip, calculate the total distance and total time: - Total distance: $6 \text{ miles (upstream)} + 6 \text{ miles (downstream)} = 12 \text{ miles}$ - Total time: $2 \text{ hours (upstream)} + 1 \text{ hour (downstream)} = 3 \text{ hours}$
Average speed is: $$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{12 \text{ miles}}{3 \text{ hours}} = 4 \text{ mph}$$
The kayaker's average rate of speed is $4$ mph.