SOLUTION: Here is another one I would need help with: Kevin was swimming agains the current, it took him 8 min. to swim 200 meters. Swimming back with the current took half as long. What is

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Question 403213: Here is another one I would need help with:
Kevin was swimming agains the current, it took him 8 min. to swim 200 meters. Swimming back with the current took half as long. What is his average swimming speed and the speed of the current?
Thank you for your help
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let k = rate of swimming without current
Let c = rate of current
k+-+c = rate of swimming against current
k+%2B+c = rate of swimming with current
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given:
(1) 200+=+%28k+-+c%29%2A8 meters
(2) 200+=+%28k+%2B+c%29%2A4 meters
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This is 2 equations and 2 unknowns, so it's solvable
(1) 8k+-+8c+=+200
(2) 4k+%2B+4c+=+200
Multiply both sides of (2) by 2
and add the equations
(1) 8k+-+8c+=+200
(2) 8k+%2B+8c+=+400
16k+=+600
k+=+37.5
and, from (2),
(2) k+%2B+c+=+50
+c+=+12.5
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Always use the definition (ave. speed) = (total distance)/(total time)
His ave. speed = %28200+%2B+200%29%2F%288+%2B+4%29+=+400%2F12
400%2F12+=+33.333 m/min
The speed of the current is 12.5 m/min