Question

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?

Answer 1

Answer:

3 mi/h

Step-by-step explanation:

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.