document.write( "Question 1062419: Against the wind a commercial airline in South America flew 540 miles in 3 hours. With a tailwind the return trip took 2.5 hours. What was the speed of the plane in still air? What was the speed of the wind? \n" ); document.write( "

Algebra.Com's Answer #677331 by ikleyn(52835) $\"\"$ $\"About$

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\n" ); document.write( "Against the wind a commercial airline in South America flew 540 miles in 3 hours. With a tailwind the return trip took 2.5 hours.
\n" ); document.write( "What was the speed of the plane in still air? What was the speed of the wind?
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document.write( "Let u be the speed of the plane (not the airline!) in miles per hour with no wind.\r\n" );
document.write( "Let v be the speed of wind.\r\n" );
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document.write( "Then\r\n" );
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document.write( " = u - v             (1)    ( = the speed of the plane flying against the wind )\r\n" );
document.write( " = u + v             (2)    ( = the speed of the plane flying with the wind )\r\n" );
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document.write( "Simplify (1) and (2):\r\n" );
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document.write( "u - v = 180,            (1')\r\n" );
document.write( "u + v = 216             (2')\r\n" );
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document.write( "Now add (1') and (2') (both sides). You will get\r\n" );
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document.write( "2u = 180 + 216  = 396  --->  u =  = 198 mph.\r\n" );
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document.write( "Thus the speed of the plane with no wind is 198 mph.\r\n" );
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document.write( "Next, from (2') v = 216 - u = 216 - 198 = 18 mph.\r\n" );
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document.write( "The speed of the wind is 18 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( "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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\n" ); document.write( "\n" ); document.write( "If after reading my solution you still have a question \"why the equations (1) and (2) have this form ?\",
\n" ); document.write( "then read the lessons above. They contain the detailed answer to this question. \r
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