Questions: Katja and Janie are paddling a canoe on a river in the direction of the current. In still water, they can paddle 1 mile in 24 minutes. The river current moves at a speed of 1 mile in 12 minutes. At what speed, in miles per hour, are Katja and Janie traveling?

Solution Steps

Katja and Janie can paddle 1 mile in 24 minutes in still water. To find their paddling speed in miles per hour, use the formula: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] Convert 24 minutes to hours: \[ 24 \text{ minutes} = \frac{24}{60} \text{ hours} = 0.4 \text{ hours} \] Now calculate the speed: \[ \text{Speed in still water} = \frac{1 \text{ mile}}{0.4 \text{ hours}} = 2.5 \text{ miles per hour} \]

The river current moves at a speed of 1 mile in 12 minutes. To find the current speed in miles per hour, use the same formula: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] Convert 12 minutes to hours: \[ 12 \text{ minutes} = \frac{12}{60} \text{ hours} = 0.2 \text{ hours} \] Now calculate the speed: \[ \text{Speed of current} = \frac{1 \text{ mile}}{0.2 \text{ hours}} = 5 \text{ miles per hour} \]

Since Katja and Janie are paddling in the direction of the current, their effective speed is the sum of their paddling speed and the speed of the current: \[ \text{Combined speed} = \text{Speed in still water} + \text{Speed of current} \] Substitute the values: \[ \text{Combined speed} = 2.5 \text{ miles per hour} + 5 \text{ miles per hour} = 7.5 \text{ miles per hour} \]

Final Answer