Nathan rafts 16 miles with the river current. at the end of 16 miles, he turns around and rafts the same distance the river current. the journey takes him 4 hours over. if he can raft at a speed of 9 mph in still water. what is the speed of the current of the river he is in?

3 mi/h

Let c represent the speed of the current. Then 9+c is Nathan's speed downriver, and 9-c is Nathan's speed upriver. He travels 16 miles each way, so his total time is given by ...

... time = distance/speed

... total time = time downriver + time upriver

For distances in miles, speeds in miles per hour, and time in hours, this is ...

... 4 = 16/(9 +c) + 16/(9 -c)

... 9² -c² = 4(9 -c) +4(9+c) . . . . . multiply by (9+c)(9-c)/4

... 81 -c² = 72 . . . . . . . . . . . . . . . simplify

... 9 = c² . . . . . . . . . . . . . . . . . . . add c²-72

... c = 3

The speed of the current in the river is 3 mi/h.

0.02040816326

6mm^3 or .6cm^3

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