SOLUTION: Hello! I am in need of an explanation for the following question I was assigned for homework. I have spent over an hour working on it but none of my solutions were correct. It goes

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Question 1055539: Hello! I am in need of an explanation for the following question I was assigned for homework. I have spent over an hour working on it but none of my solutions were correct. It goes: My motor boat normally travels at 24 kilometers per hour in still water. One day I traveled 36 kilometers against a constant current in a river. If I had traveled with the current, I would have traveled 48 km in the same time. How fast was the current? The answer is stated in the back of the book as 3 3/7 but does not give any explanation on how to get the answer. Please provide an explanation! Thank you.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
My motor boat normally travels at 24 kilometers per hour in still water. One day I traveled 36 kilometers against a constant current in a river. If I had traveled with the current, I would have traveled 48 km in the same time.
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Against current DATA:
dist = 36 km ; rate = 24 - c km/hr ; time = d/r = 36/(24-c) hr
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With current DATA:
dist = 48 km ; tate = 24+c km/hr ; time = d/r = 48/(24+c) hr
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How fast was the current?
Equation:
time = time
36/(24-c) = 48/(24+c)
3/(24-c) = 4/(24+c)
3(24+c) = 4(24-c)
72 + 3c = 96 - 4c
7c = 24
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current speed = 24/7 = 3.43 km/hr
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Cheers,
Stan H.
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