A canoeist who took 6 hours to paddle 6 miles upstream was able to return to his starting spot in 45 minutes. What was the rate of the current?

Let x be the speed of the boat in still water. Let y be the speed of the current of the river. The boat's downstream speed relative to the river bank is x + y The boat's upstream speed relative to the river bank is x - y As the boat travels 6 miles downstream in 3 hours, we have 0.75(x+y)=6

0.75x + 0.75y = 6

x + y = 8(1) As the boat travels 6 miles upstream in 6 hours, we have 6(x-y)=6

6x - 6y = 6

x - y = 1 (2)

Using the elimination method for equations 1 and 2, we get

x + y = 8

+

x - y = 1

2x = 9

x = 9/2 =4.5

but x + y = 8

therefore, 4.5 + y = 8

y = 8 - 4.5 = 3.5

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