document.write( "Question 1189570: 1. \r
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Algebra.Com's Answer #820969 by ikleyn(52803)\"\" \"About 
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\n" ); document.write( "2. A boat can go 6 miles downstream in 20 minutes, but the return trip upstream takes 30 minutes .
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document.write( "Let u represent the rate of the boat in still water and \r\n" );
document.write( "let y represent the rate of the current. \r\n" );
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document.write( "Then  the  effective speed downstream  is  u+v  miles per hour,\r\n" );
document.write( "while the  effective speed upstream    is  u-v  miles per hour.\r\n" );
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document.write( "    // It is first major point you need understand and use in this sort of problems.\r\n" );
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document.write( "Now, \"speed\" equation for boat floating downstream is the distance divided by time downstream\r\n" );
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document.write( "    \"6%2F%28%281%2F3%29%29\" = u + v        (where 1/3 represents 20 minutes = 1/3 of an hour)\r\n" );
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document.write( "or  18 = u + v.      (1)\r\n" );
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document.write( "Next, \"speed\" equation for boat floating upstream is the distance divided by time  uptream\r\n" );
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document.write( "    \"6%2F%28%281%2F2%29%29\" = u - v        (where 1/2 represents 30 minutes = 1/2 of an hour)\r\n" );
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document.write( "or  12 = u - v.      (2)\r\n" );
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document.write( "    // It is the second major point in solving such problems: you must understand and write these equation automatically !\r\n" );
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document.write( "So, you have this system of equations for u and v\r\n" );
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document.write( "    u + v =  18      (3)\r\n" );
document.write( "    u - v =  12      (4)\r\n" );
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document.write( "Now add equations (3) and (4) to eliminate \"v\". You will get\r\n" );
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document.write( "    2u = 18 + 12 = 30.     \r\n" );
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document.write( "Hence,  u = \"30%2F2\" = 15.\r\n" );
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document.write( "Thus you just found the boat' speed in still water. It is 15 miles per hour.\r\n" );
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document.write( "Next, you can find the current rate from equation (3)  \r\n" );
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document.write( "    v = 18 - u = 18 - 15 = 3 miles per hour.\r\n" );
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document.write( "Answer.  The boat' speed in still water is 15 miles per hour.\r\n" );
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document.write( "         The current speed is 3 miles per hour.\r\n" );
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document.write( "Solved.  I advise you to make the check on your own.\r\n" );
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document.write( "         After making the check, you will understand the problem and the solution MUCH better.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a typical and standard Upstream and Downstream round trip word problem.\r
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\n" ); document.write( "\n" ); document.write( "You can find many similar fully solved problems on upstream and downstream round trips with detailed solutions in lessons \r
\n" ); document.write( "\n" ); document.write( "    - Wind and Current problems \r
\n" ); document.write( "\n" ); document.write( "    - More problems on upstream and downstream round trips \r
\n" ); document.write( "\n" ); document.write( "    - Wind and Current problems solvable by quadratic equations \r
\n" ); document.write( "\n" ); document.write( "    - Unpowered raft floating downstream along a river\r
\n" ); document.write( "\n" ); document.write( "    - Selected problems from the archive on the boat floating Upstream and Downstream \r
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\n" ); document.write( "\n" ); document.write( "Read them attentively and learn how to solve this type of problems once and for all.\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the section \"Word problems\",  the topic \"Travel and Distance problems\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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        Do not pack more than one problem per post.\r
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