Question 388013: A speedboat takes 4 hours longer to go 80 miles up a river than to return. If the boat cruises at 15 miles per hour in still water, what is the rate of the current?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Start with the basic formula, Distance equals Rate times Time.
But express it as time as a function of distance and rate:
So let's talk about the downstream trip first. Going downstream the boat goes 15 mph PLUS the rate of the current, i.e.  , and the 80 mile trip is accomplished in  hours, so:
Now let's look at the upstream trip. This time the boat speed relative to the shore is 15 mph MINUS the rate of the current,  , and the 80 mile trip is accomplished in  hours, so:
A little algebra and fraction addition:
Ah ha! Now we have two things both equal to , so:
Cross-multiply, collect like terms, and put the quadratic into Standard Form.
Factor and solve. Discard the negative root -- unless you can find a river that flows upstream.
John
My calculator said it, I believe it, that settles it
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