document.write( "Question 66642: Bill rowed 30 km upstream against a 2 km/h current and back again in 8 total hours. How fast can he row in still water? \n" ); document.write( "

Algebra.Com's Answer #47305 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Bill rowed 30 km upstream against a 2 km/h current and back again in 8 total hours. How fast can he row in still water?
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\n" ); document.write( "Let s = his speed in still water
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\n" ); document.write( "Then
\n" ); document.write( "(s+2) = speed with the current
\n" ); document.write( "(s-2) = speed against the current
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\n" ); document.write( "Write a time equation: time = dist/speed; (dist given as 30):
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\n" ); document.write( "time up + time back = 8
\n" ); document.write( " $\"30%2F%28%28s-2%29%29\"$ + $\"30%2F%28%28s%2B2%29%29\"$ = 8
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\n" ); document.write( "Eliminate the denominators, mult eq by (s-2)(s+2), resulting in:
\n" ); document.write( "30(s+2) + 30(s-2) = 8(s+2)(s-2)
\n" ); document.write( "30s + 60 + 30s - 60 = 8(s^2 - 4); FOILed
\n" ); document.write( "60s = 8s^2 - 32
\n" ); document.write( "0 = 8s^2 - 60s - 32
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\n" ); document.write( "A quadratic equation:
\n" ); document.write( "8s^2 - 60s - 32 = 0
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\n" ); document.write( "Simplify, divide eq by 4
\n" ); document.write( "2s^2 - 15x - 8
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\n" ); document.write( "Factors to:
\n" ); document.write( "(2s + 1)(s - 8) = 0
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\n" ); document.write( "s = + 8 km/hr in still water is the solution we want
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\n" ); document.write( "Check:
\n" ); document.write( " 30/6 + 30/10 =
\n" ); document.write( " 5 + 3 = 8
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\n" ); document.write( "Make sense to you?
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