Description
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?
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Explanation & Answer
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
the rate of the current = y =3.5 miles/hour
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