document.write( "Question 1073014: The airspeed of a plane is its speed through the air. The groundspeed of a plane is its speed relative to the ground. The groundspeed of an airplane is affected by the speed of the wind. Suppose that a plane flying 1800 miles west requires 9 hours and flying 1800 miles east requires 6 hours. Find the airspeed of the plane and the effect wind resistance has on the plane. \n" ); document.write( "

Algebra.Com's Answer #687854 by ikleyn(52858) $\"\"$ $\"About$

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document.write( "Let u be the airspeed and v be the speed of the wind.\r\n" );
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document.write( "Then the ground-speed flying east (with the wind) is (u+v),\r\n" );
document.write( "while ground-speed flying west (against the wind) is (u-v).\r\n" );
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document.write( "The condition gives you these two equations:\r\n" );
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document.write( " = u - v   (1)   (flying west against the wind)  and\r\n" );
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document.write( " = u + v   (2)   (flying east against the wind).\r\n" );
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document.write( "It is the same as\r\n" );
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document.write( "u - v = 200,           (3)\r\n" );
document.write( "u + v = 300.           (4)\r\n" );
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document.write( "Add equations (3) and (4) (both sides). You will get\r\n" );
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document.write( "2u = 200 + 300 = 500.   Hence,  u =  = 250 miles per hour is the airspeed.\r\n" );
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document.write( "Then from (4)  u = 300 - 250 = 50 miles per hour is the speed of the wind.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\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
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\n" ); document.write( "\n" ); document.write( "In these lessons you will find the detailed solutions of many similar problems. \r
\n" ); document.write( "\n" ); document.write( "Consider them as samples. Read them attentively.\r
\n" ); document.write( "\n" ); document.write( "In this way you will learn how to solve similar 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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