document.write( "Question 1113978: Any help on this question would be greatly appreciated. The assignment is due on April 9, 2018. If you can help before then, please do. Thank you so much!\r
\n" ); document.write( "\n" ); document.write( "A boat traveling upstream goes 70 kilometers in 7 hours. If the return trip takes only 5 hours, what is the speed (in kilometers per hour) of the boat in still water? \n" ); document.write( "

Algebra.Com's Answer #728997 by ikleyn(52847) $\"\"$ $\"About$

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document.write( "Let  u  be the boat speed in still water (in kilometers per hour, km/h).\r\n" );
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document.write( "Let  v  be the rate of the current, in km/h.\r\n" );
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document.write( "Then  the boat's  effective speed downstream is  u+v  km/h,\r\n" );
document.write( "while the boat's  effective speed upstream   is  u-v  km/h.\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 upstream is \r\n" );
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document.write( " = u - v    (1)    (speed upstream = the distance divided by time upstream)\r\n" );
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document.write( "Next, \"speed\" equation for boat floating downstream is \r\n" );
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document.write( " = u + v    (2)    (speed downstream = the distance divided by time  downstream)\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( "Simplify equations (1) and (2)\r\n" );
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document.write( "u - v = 10     (3)\r\n" );
document.write( "u + v = 14     (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 = 10 + 14 = 24  ====>  u =  = 12.\r\n" );
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document.write( "Thus you just found the boat' speed in still water. It is 12 kilometers per hour.\r\n" );
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document.write( "At this point,  you just answered the problem's question.\r\n" );
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document.write( "For completeness, you can find the current rate from eq(4)  v = 14 - u = 14 - 12 = 2 km/h.\r\n" );
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document.write( "Answer.  The boat' speed in still water is 12 kilometers per hour.\r\n" );
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document.write( "         The current speed is 2 km/h.\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( "When solving such problems, you inevitably will reduce the problem to solving equations of the form (3), (4).\r
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\n" ); document.write( "\n" ); document.write( "The method of their solution I demonstrated to you is the standard version of the Elimination method.\r
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\n" ); document.write( "\n" ); document.write( "It is the simplest way/method solving such equations.\r
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\n" ); document.write( "\n" ); document.write( "And this method solving equations is the third major point of the whole procedure . . .\r
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\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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\n" ); document.write( "\n" ); document.write( "The lessons to learn from this solution :\r
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document.write( "    1.  Expressions  u+v  and  u-v  for the effective downstream and upstream speeds.\r\n" );
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document.write( "    2.  \"Speed\" equations.\r\n" );
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document.write( "    3.  The solution method to system of equation.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you know these major points - you know how to solve it !\r
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