document.write( "Question 1145947:
\n" ); document.write( "Meg rowed her boat upstream a distance of 15 mi and then rowed back to the starting point. The total time of the trip was 16 hours. If the rate of the current was 7 mph, find the average speed of the boat relative to the water. \n" ); document.write( "

Algebra.Com's Answer #767217 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "Let  \"x\"  be the average speed of the boat relative to the water (usually called as a \"boat speed in still water\"), in miles per hour.\r\n" );
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document.write( "Then the speed of the boat downstream is (x+7) mph, and the time traveling 48 miles downstream is   hours.\r\n" );
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document.write( "     The speed of the boat   upstream is (x-4) mph, and the time traveling 48 miles   upstream is   hours.\r\n" );
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document.write( "Total time for the round trip is 16 hours (given !), which gives you the \"time\" equation\r\n" );
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document.write( "     +  = 16    hours.     (1)\r\n" );
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document.write( "It is your basic equation to solve.\r\n" );
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document.write( "Multiply equation  (1)  by  (x-7)*(x+7) = . You will get\r\n" );
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document.write( "    15*(x+7) + 15*(x-7) = 16*(x^2-49).\r\n" );
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document.write( "Simplify it step by step.\r\n" );
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document.write( "    15x + 15*7 + 15x - 15*49 = 16x^2 - 784\r\n" );
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document.write( "    16x^2 - 30x - 784 = 0.\r\n" );
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document.write( "Apply the quadratic formula\r\n" );
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document.write( "     =  = .\r\n" );
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document.write( "Only positive root  x =  = 8  makes sense.\r\n" );
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document.write( "Answer.  The boat speed in still water is 8 miles per hour.\r\n" );
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document.write( "CHECK.   Let's check equation (1). Its left side is\r\n" );
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document.write( "          +  =  +  = 15 + 1 = 16 hours - same as the given total time.   ! The solution is correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is very standard and typical round trip upstream and downstream Travel and Distance problem.\r
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\n" ); document.write( "\n" ); document.write( "See the 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
\n" ); document.write( "\n" ); document.write( "in this site, where you will find other similar solved problems with detailed explanations.\r
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\n" ); document.write( "\n" ); document.write( "Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.
\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( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\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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