Nicholas paddles his canoe downstream from the lodge to the park in 44 hours and then back upstream to the lodge in 55 hrs. If the distance from the lodge to the park is 3030 miles, find Nicholas' speed in still water and the speed of the current.

Nicholas' speed: 61.9772 miles/hour

current's speed: 6.8864 miles/hour

Explanation:

Let's call Nicholas's speed "x", and the current speed "y".

Going downstream, the total speed is x+y, and we can formulate the equation:

(x+y)*44 = 3030 -> x+y =  68.8636 miles/hour

Going upstream, the total speed is x-y, and we can formulate the equation:

(x-y)*55 = 3030 -> x-y =  55.0909 miles/hour

If we sum both equations, we have that:

2x = 123.9545

x = 61.9772 miles/hour

Now, to know the current speed, we just apply "x" value in one of the equations:

x+y = 68.8636 -> 61.9772 + y = 68.8636 -> y = 6.8864 miles/hour

it is a negative acceleration

well clustered together.

points close on a scatter diagram