Question 1158748: A kayak can travel 18 miles downstream in 3 hours, while it would take 9 hours to make the same trip upstream. Find the speed of the kayak in still water, as well as the speed of the current. Let k represent the speed of the kayak in still water, and let c represent the speed of the current.
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
From the condition, you have these two equations
18/3 = 6 = k + c (1) (the effective speed downstream)
18/9 = 2 = k - c (2) (the effective speed upstream)
Again, you have these two equations
k + c = 6 (1)
k - c = 2 (2)
Add these two equations. You will get
2k = 6 + 2 = 8; hence k = 8/2 = 4 is the speed of the kayak in still water.
Next, substitute k= 4 into equation (1). You will get
4 + c = 6, which implies c = 6-4 = 2.
ANSWER. The kayak speed in still water is 4 miles per hour.
The speed of the current is 2 miles per hour.
Solved.
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