Paddling with the current in a river, jake traveled 16 miles. Even though he paddled upstream for an hour longer than the amount of the time he paddled downstream jake could only travel 6 miles against the current. I'm still waterJake paddles at a rate of 5 mph. What is the speed of the current I the river

the rate of the current is 3 mph.

Step-by-step explanation:

Let x represent the rate of the current.

In still water, Jake paddles at a rate of 5 mph. Paddling with the current in a river, Jake traveled 16 miles. It means that the speed with which she travelled downstream (with the current) is (5 + x) mph

Time = distance/speed

Time spent in paddling downstream is

16/(5 + x)

While paddling upstream, it took an hour longer. The speed with which he paddled upstream is (5 - x) mph.

Jake could only travel 6 miles against the current. It means that the time spent in travelling upstream us

6/(5 - x)

Since it took 1 hour longer, then

6/(5 - x) = 16/(5 + x) + 1

Cross multiplying by (5 - x)(5 + x), it becomes

6(5 + x) = 16(5 - x) + 1(5 + x)(5 - x)

30 + 6x = 80 - 16x + 25 - 5x + 5x - x²

30 + 6x = - x² - 16x + 5x - 5x + 25 + 80

30 + 6x = - x² - 16x + 105

x² + 16x + 6x + 30 - 105 = 0

x² + 22x - 75 = 0

x² + 25x - 3x - 75 = 0

x(x + 25) - 3(x + 25) = 0

x - 3 = 0 or x + 25 = 0

x = 3 or x = - 25

Since x cannot be negative, then x = 3 mph

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.