document.write( "Question 1204016: A motorboat takes 4 hours to travel 128 kilometers going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? \n" ); document.write( "

Algebra.Com's Answer #840000 by ikleyn(52810) $\"\"$ $\"About$

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\n" ); document.write( "A motorboat takes 4 hours to travel 128 kilometers going upstream.
\n" ); document.write( "The return trip takes 2 hours going downstream. What is the rate of the boat in still water
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document.write( "Let  u  be the motorboat 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 = 32     (3)\r\n" );
document.write( "u + v = 64     (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 = 32 + 64 = 96  ====>  u =  = 48.\r\n" );
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document.write( "Thus you just found the boat' speed in still water. It is 48 kilometers per hour.\r\n" );
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document.write( "Now find the current rate from equation (4)  v = 64 - u = 64 - 48 = 16 km/h.\r\n" );
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document.write( "Answer.  The boat' speed in still water is 48 kilometers per hour.\r\n" );
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document.write( "         The current speed is 16 km/h.\r\n" );
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Post-solution note

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\n" ); document.write( "\n" ); document.write( "        I solved the problem formally, and this formal answer and the solution both are correct.\r
\n" ); document.write( "\n" ); document.write( "        But you should keep in your mind the following.\r
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\n" ); document.write( "\n" ); document.write( "        In this problem, the speed of the motorboat in still water is very high: 48 km/h.\r
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\n" ); document.write( "\n" ); document.write( "        Even if imagine so high speed, it will mean that the river is lowland.\r
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\n" ); document.write( "\n" ); document.write( "        But for lowland river, the current rate of 16 km/h is too high.\r
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\n" ); document.write( "\n" ); document.write( "        So, the input data in this problem are not realistic.\r
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\n" ); document.write( "\n" ); document.write( "        I wrote this post-solution note to explain this fact to you.\r
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\n" ); document.write( "\n" ); document.write( "                When a professional Math composer creates his (or her) problems, usually he (or she) \r
\n" ); document.write( "\n" ); document.write( "                knows a subject good enough to avoid (= to exclude) such inconsistencies.\r
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\n" ); document.write( "\n" ); document.write( "                Because he (or she) does think on what he (or she) is doing.\r
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