SOLUTION: A boat can go 33 mph in still water. It takes as long to go 300 miles upstream as it does to go downstream 360 miles. how fast is the current?
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Question 250597: A boat can go 33 mph in still water. It takes as long to go 300 miles upstream as it does to go downstream 360 miles. how fast is the current?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let 
represent the rate of the current.
When the boat is going upstream, against the current, it is going 33 mph through the water, but 
mph with respect to the riverbed or the bank of the river or whatever fixed thing you are using to measure the distance traveled against. Likewise, when the boat is going downstream, it is travelling 
mph with respect to the riverbed.
Remember that distance equals rate times time, or 
. Solving this equation time in terms of distance and rate yields:
Now let's substitute some values from the problem. To describe the upstream trip:
And for the downstream trip:
But since we know that the time for each of the trips was the same ("It takes as long..."), we can now write:
Now all you have to do is cross-multiply the proportion and solve for .
John
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