document.write( "Question 1073597: A turbo-prop plane flying with the wind flew 2100 mi in 5 h. Flying against the wind, the plane required 7 h to travel the same distance. Find the rate of the wind and the rate of the plane in calm air. \n" ); document.write( "

Algebra.Com's Answer #688390 by ikleyn(52799) $\"\"$ $\"About$

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document.write( "Let \"u\" be the speed of the plane at no wind (=same as in calm air), in mph.\r\n" );
document.write( "Let \"v\" be the speed of wind.\r\n" );
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document.write( "Then the effective speed of the plane flying WITH the wind is (u+v) mph (relative to the ground).\r\n" );
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document.write( "the effective speed of the plane flying AGAINST the wind is (u-v) mph (relative to the ground).\r\n" );
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document.write( "According to the condition, \r\n" );
document.write( "the plane effective speed is  = 420 mph flying  with    the wind,\r\n" );
document.write( "and       effective speed is  = 300 mph flying  against the wind.\r\n" );
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document.write( "It gives you two equations \r\n" );
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document.write( "u + v = 420,    (1)\r\n" );
document.write( "u - v = 300.    (2)\r\n" );
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document.write( "Add the two equations (both sides). You will get\r\n" );
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document.write( "2u = 420 + 300 = 720.   Hence,  u =  = 360.\r\n" );
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document.write( "Thus the speed of the plane at no wind is 360 mph.\r\n" );
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document.write( "Next, from the equation (1) v = 420 - u = 420 - 360 = 60 mph.\r\n" );
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document.write( "Thus the speed of the wind  is 60 mph.\r\n" );
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document.write( "Answer.  The speed of the plane at no wind is 360 mph.\r\n" );
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document.write( "         The speed of the wind  is 60 mph.\r\n" );
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document.write( "Check.  The speed of the plane with the wind is 360 + 60 = 420 mph, and the flight time is  = 5 hours.\r\n" );
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document.write( "        The speed of the plane against the wind is 360 - 60 = 300 mph, and the flight time is  = 7 hours.\r\n" );
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document.write( "        Checks !\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
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\n" ); document.write( "\n" ); document.write( "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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