document.write( "Question 1141756: Matt and Anna Killian are frequent fliers on Fast-n-Go Airlines. They often fly between two cities that are a distance of 1980 miles apart. On one particular trip, they flew into the wind and the trip took 5.5 hours. The return trip with the wind behind them, only took about 4.5 hours. Find the speed of the wind and the speed of the plane in still air. \n" ); document.write( "

Algebra.Com's Answer #762384 by ikleyn(52848) $\"\"$ $\"About$

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document.write( "Flying with the wind, their effective speed (the ground speed) was\r\n" );
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document.write( "     = 440 miles per hour.\r\n" );
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document.write( "This effective speed is the sum of the airplane speed \"u\" and the wind speed \"v\":\r\n" );
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document.write( "    u + v = 440.     (1)\r\n" );
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document.write( "Flying against the wind, their effective speed (the ground speed) was\r\n" );
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document.write( "     = 360 miles per hour.\r\n" );
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document.write( "This effective speed is the DIFFERENCE of the airplane speed \"u\" and the wind speed \"v\":\r\n" );
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document.write( "    u - v = 360.     (2)\r\n" );
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document.write( "Thus you have two equations (1) and (2) to determine two unknowns, u and v.\r\n" );
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document.write( "Add the equations (1) and (2), and you will get\r\n" );
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document.write( "    2u = 440 + 360 = 800  ====>  u = 800/2 = 400 mph.\r\n" );
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document.write( "It is the airplane speed at no wind.\r\n" );
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document.write( "Next, substitute the found value of   \"u\"  into equation (1) to find  \"v\"\r\n" );
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document.write( "    400 + v = 440  ====>  v = 440 - 400 = 40 mph.\r\n" );
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document.write( "ANSWER.  The airplane speed at no wind is 400 mph.  The wind speed is 40 mph.\r\n" );
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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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