document.write( "Question 1179658: A plane traveling with the wind flew 1312.5 mi in 5.25 h. Against the wind, the plane required 6.25 h to fly the same distance. Find the rate of the plane in calm air and the rate of the wind. \n" ); document.write( "

Algebra.Com's Answer #853619 by ikleyn(53619) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "A plane traveling with the wind flew 1312.5 mi in 5.25 h.
\n" ); document.write( "Against the wind, the plane required 6.25 h to fly the same distance.
\n" ); document.write( "Find the rate of the plane in calm air and the rate of the wind.
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\n" ); document.write( "\n" ); document.write( "        The solution in the post by @mananth is incorrect: it has arithmetic errors.\r
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\n" ); document.write( "\n" ); document.write( "        Not only is it technically unsuitable, but it is also unsuitable in its design.\r
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\n" ); document.write( "\n" ); document.write( "        In this my post, I provide short and straightforward solution to the given problem.\r
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document.write( "Let x be the rate of the plane in calm air, in miles per hour.\r\n" );
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document.write( "Let y be the rate of the wind.\r\n" );
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document.write( "Then  the effective speed of the plane with    the wind is (x+y) mph,\r\n" );
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document.write( "while the effective speed of the plane against the wind is (x-y) mph,\r\n" );
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document.write( "From the problem, the effective rate of the plane with the wind is  the distance divided by the travel time\r\n" );
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document.write( "     = 250 miles per hour,\r\n" );
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document.write( "and the effective rate of the plane against the wind is  the distance divided by the travel time\r\n" );
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document.write( "     = 210 miles per hour.\r\n" );
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document.write( "So, we have these two equations\r\n" );
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document.write( "    x + y = 250     (1)\r\n" );
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document.write( "    x - y = 210     (2)\r\n" );
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document.write( "To find x, add the equation.  You will get\r\n" );
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document.write( "    2x = 250 + 210 = 460,  x = 460/2 = 230.\r\n" );
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document.write( "Now express y from equation (1) and calculate\r\n" );
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document.write( "    y = 250 - x = 250 - 230 = 20.\r\n" );
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document.write( "At this point the problem is solved completely.\r\n" );
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document.write( "ANSWER.  The speed of the plane in calm air is 230 mph.  The rate of the wind is 20 mph.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "I placed this my solution here as an opposite alternative to the solution by @mananth.\r
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\n" ); document.write( "\n" ); document.write( "Now I will explain you, why I think that my solution is better than that of @mananth.\r
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\n" ); document.write( "\n" ); document.write( "The @mananth solution is more long way reasoning and calculations than it is necessary.
\n" ); document.write( "My solution is straightforward and contains only necessary reasoning and calculations.\r
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\n" ); document.write( "\n" ); document.write( " Everything which is not effective and straightforward, is filtered out.\r
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\n" ); document.write( "\n" ); document.write( "The school education always prefers more straightforward and short reasoning, explanations and calculations,
\n" ); document.write( "because the goal of solving such problems is not only getting a correct answer.\r
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\n" ); document.write( "\n" ); document.write( "A true goal of solving such problems is to teach students to organize
\n" ); document.write( "and present their thoughts and their arguments in adequate form.\r
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\n" ); document.write( "\n" ); document.write( "@mananth does it his way only because his computer code, which he permanently uses to create the solution file,
\n" ); document.write( "is written this way - but his way is not effective.\r
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\n" ); document.write( "\n" ); document.write( "It is why I prepared and placed here my solution to provide a better way
\n" ); document.write( "for you, a reader, to learn and to master this subject.\r
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\n" ); document.write( "\n" ); document.write( "What I wrote here are not empty words.
\n" ); document.write( "Today, on Jan.21, 2026 I looked on how artificial intelligence treats this problem.
\n" ); document.write( "The Google AI Overflow repeats this long process, copying the style of @mananth.
\n" ); document.write( "Thus, thousands of schoolchildren will suffer and will not know how to correctly present
\n" ); document.write( "their thoughts and how to correctly present a solutions to such problems.\r
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\n" ); document.write( "\n" ); document.write( "And this is already a national-scale problem - when AI is copying from badly written sources.\r
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