Question

Huck finn used a canoe to go up and down the river. it took him 2 hours to travel 16 miles down the river and 4 hours to go back up to where he started. how fast (in mph) is the current of the river in mph? how fast (in mph) does he paddle?

Answer 1

Huck paddles at a speed of 6 mph in still water, and the current of the river is 2 mph. This problem requires setting up equations for travel downstream and upstream, then solving for the two unknowns.

Step-by-step explanation:

The student's problem is a classic example of relative motion and can be solved using the concepts of rate, time, and distance, typically covered in high school mathematics courses.

To find the speed of the current of the river and the paddling speed of Huck, we set up two equations based on the given information: one for the downstream trip and one for the upstream trip.

Let's denote Huck's paddling speed in still water as 'p' and the speed of the current as 'c'. When Huck travels downstream, the current aids his paddling, so his effective speed is 'p + c'. Conversely, when traveling upstream, the current opposes his motion, making his effective speed 'p - c'.

Downstream, Huck covers 16 miles in 2 hours: 16 = 2(p + c). Upstream, Huck covers the same distance (16 miles) in 4 hours: 16 = 4(p - c). Solving these two equations simultaneously gives us the values for 'p' and 'c'.

1. Dividing the downstream distance by the time gives 16 miles / 2 hours = 8 mph for p + c.
2. Dividing the upstream distance by the time gives 16 miles / 4 hours = 4 mph for p - c.
3. Adding these two equations (1 and 2) we get: 8 mph + 4 mph = 2p, which means p = 6 mph.
4. Subtracting equation 2 from equation 1, we get: 8 mph - 4 mph = 2c, which means c = 2 mph.

Therefore, Huck paddles at a speed of 6 mph in still water, and the current of the river is 2 mph.