Question 79553: This is a problem my teacher made up and I'm getting stuck after I set up the table.
In a total of 2 hours, a tugboat traveled upriver 5 miles and returned. If the river's current is 4 miles per hour, find the speed of the tugboat in still water. Round your answer to the nearest 0.1 mi/hr if necessary.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a total of 2 hours, a tugboat traveled upriver 5 miles and returned. If the river's current is 4 miles per hour, find the speed of the tugboat in still water.
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Upstream DATA:
distance= 5 miles ; time=x hrs ; rate = d/t= 5/x mph
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Downstream DATA:
distance=5 miles; time=(2-x) hrs ; rate = d/t = 5/(2-x) mph
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EQUATIONS:
Let speed of boat in still water be "b".
Remember the speed of the current is 4 mph.
Upstream the rate is 5/x=b-4
Downstream the rate is 5/(2-x)=b+4
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Subtract the 1st equation from the 2nd to get:
5/(2-x)-(5/x)=8
Multiply thru by (2-x)x to get:
5x-10+5x=8x(2-x)
10x-10=16x-8x^2
8x^2-6x-10=0
4x^2-3x-5=0
x=[3+-sqrt(9-4*4*-5)]/8
x=[3+-sqrt(89)]/8
x=1.55 hrs
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Substitute to solve for b:
5/1.55=b-4
b=4+3.22
b=7.22 mph (the speed of the boat in still water)
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Cheers,
Stan H.
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