document.write( "Question 1137928: A plane travels at a speed of 175mph in still air. Flying with a tailwind, the plane is clocked over a distance of 1000 miles. Flying against a headwind, it takes 1 hour longer to complete the return trip. What was the wind velocity? \n" ); document.write( "

Algebra.Com's Answer #755794 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let w be the wind velocity (in miles per hour).\r\n" );
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document.write( "Then the plane' speed with the wind is (175 + w) miles per hour,\r\n" );
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document.write( "and the time to fly 1000 miles with the wind is   hours.\r\n" );
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document.write( "Also, the plane' speed against the wind is (175 - w) miles per hour,\r\n" );
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document.write( "and the time to fly 1000 miles against the wind is   hours.\r\n" );
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document.write( "Now you can write the \"time\" equation\r\n" );
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document.write( "      -  = 1 hour\r\n" );
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document.write( "saying that  \"it takes 1 hour longer to complete the return trip\".\r\n" );
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document.write( "It is your basic equation.  To solve it, multiply both sides by (175+w)*(175-w).  You will get\r\n" );
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document.write( "    1000(175+w) - 1000(175-w) = 175^2 - w^2,   or\r\n" );
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document.write( "    2*1000*w = 175^2 - w^2\r\n" );
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document.write( "    w^2 + 2000w - 175^2 = 0\r\n" );
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document.write( "      =  = .\r\n" );
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document.write( "Only positive value of the roots is meaningful:  w =  = 15.197.\r\n" );
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document.write( "ANSWER.  The wind' speed is 15.197 miles per hour.\r\n" );
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document.write( "CHECK.   = 1 hour.   ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered, checked and completed.\r
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\n" ); document.write( "\n" ); document.write( "It is a typical \"tailwind and headwind\" word 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( "    - Wind and Current problems solvable by quadratic equations \r
\n" ); document.write( "\n" ); document.write( "    - Selected problems from the archive on a plane flying with and against the wind \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( "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
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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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