SOLUTION: Use a system of equations in two variables to solve each problem. I already know that the answer is 1 mph. Can you help me determine how? A kayaker can paddle 8 miles down a r

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Question 328962: Use a system of equations in two variables to solve each problem. I already know that the answer is 1 mph. Can you help me determine how?
A kayaker can paddle 8 miles down a river in 2 hours and make the return trip in 4 hours. Find the speed of the current in the river.
Found 2 solutions by nyc_function, Alan3354:
Answer by nyc_function(2741) (Show Source):
You can put this solution on YOUR website!
Use D = rt.
Let d = speed of the river's current
GOING TRIP:
rate = s + d
time = 2 hours
distance = 8 miles
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RETURN TRIP:
rate = s - d
time = 4 hours
distance = 8 miles
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2(s + d) = 8
4(s - d) = 8
2s + 2d = 8
4s - 4d = 8
4s = 4d + 8
s = (4d + 8)/4
s = d + 2
2(d + 2) + 2d = 8
2d + 4 + 2d = 8
4d + 4 = 8
4d = 8 - 4
4d = 4
d = 4/4
d = 1

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Speed downstream = 8/2 = 4 mph
Speed upstream = 8/4 = 2 mph
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The kayak's speed relative to the water is the average, = (4+2)/2 = 3 mph
The current is the difference, 4-3 = 1 mph