SOLUTION: sammy owns a motor boat that travels 4 miles/hour in still water. It goes 12 miles upstream and 12 miles back again (downstream) in a total of 8 hours. Find the speed of the curren

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Question 326282: sammy owns a motor boat that travels 4 miles/hour in still water. It goes 12 miles upstream and 12 miles back again (downstream) in a total of 8 hours. Find the speed of the current of the river.
I need help setting up the equation in proportion form. Thanks!
Found 2 solutions by scott8148, solver91311:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
time = distance / rate

[12 / (4 - c)] + [12 / (4 + c)] = 8

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the idea that distance = rate times time



Which can also be expressed:



We know that , and we know that the rate in still water that we'll call . Let be the rate of the current. And let represent the amount of time required to make the upstream trip. That means the amount of time required for the downstream trip is . When the boat is going upstream, the current is against the boat, so the actual rate is . Downstream the current adds, so .

Now we can model the two trips, first the upstream:



and the downstream:



The rest is just a little algebra:







Then:















Ignore the negative root since we are reasonably certain that the current wasn't going backwards.

John