Two friends spend an afternoon canoeing on a river. They first paddle 5 miles upstream (fighting the current), and then 5 miles back downstream (with the current).

Question

Their average paddling speed is 4 mph, and the entire trip takes a total of 3 hours.

A) find the speed of the river, x

B) if the river was stagnant and x=0, what would be the minimum amount of time it would take to paddle up and down the river?

C) what percentage of the trip was spent going upriver vs downriver?

D) look at your rational function. The speed of the river x cannot be all real numbers. Thjnk if the mechanics of the problem: there must be a logical minimum and maximum speed to the river. If your paddling upriver at 4mph and you manage to reach the top against the current, what must the maximum value of the rivers speed be? What is happening at this value on the graph?

Answer 1

4(3) = 12 miles round trip, 6 miles each way

distance = speed times time, d=rt

speed of river current = 1.5 mph

speed in stagnant water = 4.5 mph to go 12 miles round trip would take minimum 12/4.5 = 2 2/3 hours

twice as much time was spent going upstream. 1/3 of the time was downstream or 33 1/3 % of the time

2/3 or 66 2/3 % of the time was going upstream

(4.5 + 1.5)(1 hour = 6 miles downstream

(4.5-1.5)(2 hours) = 6 miles upstream