You can put this solution on YOUR website! The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water?
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Let s = speed of the boat in still water
Then:
(s-3) = speed up-river
and
(s+3) = speed down-river
:
Write a time equation: Time = distance/speed
:
Time up-river + Time down-river = 9 hrs + = 9
;
Multiply equation by (s+3)(s-3) and you have:
:
60(s+3) + 60(s-3) = 9(s+3)(s-3)
:
60s + 180 + 60s - 180 = 9(s^2 - 9)
:
120s = 9s^2 - 81
:
9s^2 - 120s - 81 = 0; a quadratic equation
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Use the quadratic equation to find s: a=9; b=-120; c=-81
:
:
:
Do the math, you should get a positive solution of:
:
s = 13.977 mph, speed in still water
:
:
Check on calc, find the times at each speed:
60/16.977 + 60/10.977 = 9.00 hrs
You can put this solution on YOUR website! The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water?
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Let the speed of the boat in still water be "b"
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Upriver DATA:
distance = 60 mi ; rate = b-3 mph ; time = d/r = 60/(b-3) hrs.
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Downriver DATA:
distance = 60 mi; rate = b+3 ; time = d/r = 60/(b+3) hrs.
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EQUATION:
time up + time down = 9 hrs
60/(b-3) + 60/(b+3) = 9
Divide thru by 60 to get:
1/(b-3) + 1/(b+3) = 3/20
Multiply thru by 20(b-3)(b+3) to get:
20(b+3) + 20(b-3) = 3(b^2-9)
40b=3b^2-27
3b^2-40b-27=0
b=[40+-sqrt(40^2-4*3*-27)]/6
b=[40+-2sqrt(491)]/6
Positive Answer: b=14.0528 mph (this is the speed of the boat in still water)
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Cheers,
Stan H.
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