SOLUTION: the current of a stream moves at 5 mph. a boat travels 31 mi upstream and 31 mi down stream in a total time if 20 hours what is the speed of the boat in still water?

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Question 864811: the current of a stream moves at 5 mph. a boat travels 31 mi upstream and 31 mi down stream in a total time if 20 hours what is the speed of the boat in still water?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
the current of a stream moves at 5 mph. a boat travels 31 mi upstream and 31 mi down stream in a total time if 20 hours what is the speed of the boat in still water?
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let x=speed of boat in still water.
x+5=speed of boat downstream.
x-5=speed of boat upstream.
travel time=distance/speed
31%2F%28x%2B5%29%2B31%2F%28x-5%29=20
LCD:(x+5)(x-5)
31%28x-5%29%2B31%28x%2B5%29=20%28x-5%29%28x%2B5%29
31x-155%2B31x%2B155=20%28x%5E2-25%29
62x=20x%5E2-500%29
20x^2-62x-500=0
10x^2-31x-250=0
solve for x by quadratic formula: x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=10, b=-31, c=-250
ans:
x≈6.78
speed of the boat in still water? 6.78 mph