SOLUTION: the speed of a boat in still water is 10 mph. if it travels 30 miles up stream and 30 miles down stream in a total of 10 hours what is the speed of the current?

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Question 520174: the speed of a boat in still water is 10 mph. if it travels 30 miles up stream and 30 miles down stream in a total of 10 hours what is the speed of the current?
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


The current adds to the rate going downstream and the current subtracts from the rate going upstream. Let represent the speed of the current. Let represent the time for the upstream trip, hence is the time for the downstream trip. Finally, time is equal to distance divided by rate, so:



and



A little Algebra Music, Maestro:





Now that we have two things equal to , set them equal to each other (simplifying in the process)



All that is left is to cross multiply, collect terms, and solve the resulting quadratic. Note: The quadratic does not factor, so use the quadratic formula and simplify; discard the negative root. Leave your answer in radical form unless you have been instructed elsewhere to provide a numeric approximation.

John

My calculator said it, I believe it, that settles it
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