document.write( "Question 181544This question is from textbook Fourth Edition Elementary and Intermediate Algebra
\n" ); document.write( ": 4. The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hours. What is the speed of the boat in still water?\r
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Algebra.Com's Answer #136132 by ptaylor(2198)\"\" \"About 
You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
\n" ); document.write( "Let r=speed of the boat in still water
\n" ); document.write( "r-5=patrol boat's rate upstream (against the current)
\n" ); document.write( "and r+5=patrol boat's rate downstream (with the current)
\n" ); document.write( "Time travelling upstream =40/(r-5)
\n" ); document.write( "Time travelling downstream=40/(r+5)
\n" ); document.write( "And we are told that the above times add up to 6 hr
\n" ); document.write( "So:
\n" ); document.write( "40/(r-5) + 40/(r+5)=6 multiply each term by (r-5)(r+5)
\n" ); document.write( "40(r+5)+40(r-5)=6(r+5)(r-5) get rid of parens
\n" ); document.write( "40r+200+40r-200=6r^2-150 simplify
\n" ); document.write( "80r=6r^2-150 divide each term by 2
\n" ); document.write( "40r=3r^2-75 subtract 40r from each side
\n" ); document.write( "3r^2-40r-75=0 quadratic in standard form and it can be factored:\r
\n" ); document.write( "\n" ); document.write( "(3r+5)(r-15)=0
\n" ); document.write( "r=15--------------------------answer
\n" ); document.write( "and
\n" ); document.write( "r=-5/3-----------------disregard negative value for rate---in this problem, rate is positive\r
\n" ); document.write( "\n" ); document.write( "CK
\n" ); document.write( "40/10 +40/20=6
\n" ); document.write( "4+2=6
\n" ); document.write( "6=6\r
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor
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