document.write( "Question 484993: A boat can travel 5 miles upstream and 5 miles downstream in a total of 6 hours. If the speed of the current is 2 miles per hour, what is the speed of the boat in still water?
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Algebra.Com's Answer #331798 by emargo19(101) $\"\"$ $\"About$

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Let s = speed in still water
\n" ); document.write( "Then
\n" ); document.write( "(s+2) = speed down-stream
\n" ); document.write( "and
\n" ); document.write( "(s-2) = speed up-stream
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\n" ); document.write( "Write a time equation; Time = dist/speed
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\n" ); document.write( "Time up-stream + time down-stream = 6 hrs
\n" ); document.write( " $\"5%2F%28%28s-2%29%29\"$ + $\"5%2F%28%28s%2B2%29%29\"$ = 6
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\n" ); document.write( "Multiply equation by (s-2)(s+2) and you have:
\n" ); document.write( "5(s+2) + 5(s-2) = 6(s-2)(s+2)
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\n" ); document.write( "5s + 10 + 5s - 10 = 6(s^2 - 4)
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\n" ); document.write( "5s + 5s + 10 - 10 = 6s^2 - 24
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\n" ); document.write( "10s = 6s^2 - 24
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\n" ); document.write( "0 = 6s^2 - 10s - 24
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\n" ); document.write( "Simplify divide equation by 2 and you have:
\n" ); document.write( "3s^2 - 5s - 12 = 0
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\n" ); document.write( "Factors to
\n" ); document.write( "(3s + 4 )(s - 3) = 0
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\n" ); document.write( "s = +3 mph in still water, (it's the positive solution we want here)
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\n" ); document.write( "Check using time: speed upstream (3-2)= 1 mph; speed down (3+2) = 5 mph
\n" ); document.write( "5/1 = 5 hrs upstream
\n" ); document.write( "5/5 = 1 hr downstream
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\n" ); document.write( "total 6 hrs as given \n" ); document.write( "

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