Question 205883: A boat travels 12 miles upstream and then turns around and travels 12 miles downstream. The total time for both trips is 3 hours. If the stream flows at 1 mph, how fast does the boat travel in still water? Round the answer to the nearest tenth.
Answer by mickclns(59)   (Show Source):
You can put this solution on YOUR website! Here's one that is very similar. Figure out how it works and you will have figured how to work your problem:
The question:
a boat traveled 210 miles downstream and back. the trip downstream took 10 hours. the trip back took 70 hours. Find the speed of the boat in still water and the speed of the current.
The answer:
Let c be the speed of the current and b the speed of the boat in still water (we assume this speed is constant)
D=RT, distance = rate x time
the distance is 210 in each direction
the rate downstream (current pushing the boat forward) is b+c
the rate upstream (current dragging against the boat) is b-c
210 = (b+c) x 10 (downstream)
210 = (b-c) x 70 (upstream)
dividing both sides of top equation by 10 and bottom equation by 70 we have
21 = b+c
3 = b-c
adding the left & right sides of the top equation to L&R sides of bottom equation, we have
24 = 2b (eliminating c)
b = 12 and
c=9, since 3 = 12-c
So, the speed of the boat in still water is 12 mph and the speed of the current is 9 mph
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