SOLUTION: A boat goes upstream 600 m, moving 30 m/min through the water. The boat travels back downstream to the starting point, this time only going 20 m/min through the water. The total ti

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Question 426820: A boat goes upstream 600 m, moving 30 m/min through the water. The boat travels back downstream to the starting point, this time only going 20 m/min through the water. The total time spent is 75 minutes. How fast was the current flowing?
Answer by Alan3354(69443) About Me  (Show Source):
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A boat goes upstream 600 m, moving 30 m/min through the water. The boat travels back downstream to the starting point, this time only going 20 m/min through the water. The total time spent is 75 minutes. How fast was the current flowing?
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b = boat's speed relative to the water
c = current
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Upstream + downstream = 75 mins
600/(30 - c) + 600/(20 + c) = 75
One equation and one variable
600%2820%2Bc%29+%2B+600%2830-c%29+=+75%2820%2Bc%29%2830-c%29+=+75%28600%2B10c-c%5E2%29
8%2820%2Bc%29+%2B+8%2830-c%29+=+%28600%2B10c-c%5E2%29
160+%2B+240+=+%28600%2B10c-c%5E2%29
c%5E2+-+10c+-+200+=+0
(c-20)*(c+10) = 0
c = 20 m/min