document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84762>Question 84762</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to solve this word problem in the form of a quadratic equation and am having difficulty. Please help me.<BR>\n" );
document.write( "Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed of her boat in still water is 9 km/hr. Find the speed of the stream.<BR>\n" );
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document.write( "Let the speed of the stream = 'x' km/hr\r<BR>\n" );
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document.write( "speed of the boat = 9km/hr\r<BR>\n" );
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document.write( "Relative Speed upstream = (9-x) km/hr\r<BR>\n" );
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document.write( "Relative speed downstream = (9+x) km/hr\r<BR>\n" );
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document.write( "Distance travelled = 12 km up and 12 km down\r<BR>\n" );
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document.write( "Time taken for upward journey = distance/speed\r<BR>\n" );
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document.write( "                              = 12/(9-x) hrs\r<BR>\n" );
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document.write( " Time taken for downward journey = distance/speed\r<BR>\n" );
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document.write( "                              = 12/(9+x) hrs\r<BR>\n" );
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document.write( "Total time taken given to be = 3 hrs\r<BR>\n" );
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document.write( "==> 12/9-x  + 12/9+x = 3\r<BR>\n" );
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document.write( "==> 12(9+x) + 12(9-x) = 3(9+x)(9-x)\r<BR>\n" );
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document.write( "==> 108 + 12x + 108 - 12x = 3(81 - x^2)[as (a+b)(a-b) = a^2-b^2)]\r<BR>\n" );
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document.write( "==> 216 = 243 - 3x^2\r<BR>\n" );
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document.write( "==> 3x^2 = 243 - 216\r<BR>\n" );
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document.write( "==> 3x^2 = 27\r<BR>\n" );
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document.write( "==> x^2 = 27/3\r<BR>\n" );
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document.write( "        = 9\r<BR>\n" );
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document.write( "==> x = 3\r<BR>\n" );
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document.write( "Thus the speed of the boat = 3 km/hr\r<BR>\n" );
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document.write( "Good Luck!!!<BR>\n" );
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