SOLUTION: Sam kayaked 3 miles downstream, then paddled back upstream to his starting place. If the total trip took 4 hours, and the current in the stream was 0.4 miles per hour, at what spee
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Question 91226: Sam kayaked 3 miles downstream, then paddled back upstream to his starting place. If the total trip took 4 hours, and the current in the stream was 0.4 miles per hour, at what speed can Sam paddle his kayak in still water? (use the quadratic method to solve) Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Sam kayaked 3 miles downstream, then paddled back upstream to his starting place. If the total trip took 4 hours, and the current in the stream was 0.4 miles per hour, at what speed can Sam paddle his kayak in still water? (use the quadratic method to solve)
:
Let x = his speed in still water:
Then
(x+.4) = speed down-stream
(x-.4) = speed up-stream
:
Write a time equation: time = dist/speed
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Time downstream + time up-stream = 4 hrs + = 4
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Multiply equation by (x-.4)(x+.4) to get rid of the denominators
3(x-.4) + 3(x+.4) = 4(x+.4)(x-.4)
:
3x - 1.2 + 3x + 1.2 = 4(x^2 - .16)
:
6x = 4x^2 - .64
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The quadratic equation:
4x^2 - 6x - .64 = 0
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Use the quadratic formula: a=4; b=-6; c=-.64
:
:
:
:
: ; we only care about the positive solution here
:
:
x = 1.6 mph in still water
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Check solution:
upstream: 1.6-.4 = 1.2
downstream: 1.6 + .4 = 2.0 + =
1.5 + 2.5 = 4
