document.write( "Question 1088980: a plane flew720 mi in 3 hr with the wind. it would take 4 hr to travel the same distance against the wind. what is the rate of the plane in still air and the rate of wind? \n" ); document.write( "

Algebra.Com's Answer #703310 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "a plane flew 720 mi in 3 hr with the wind. it would take 4 hr to travel the same distance against the wind.
\n" ); document.write( "what is the rate of the plane $\"highlight%28cross%28in_still_air%29%29\"$ at no wind and the rate of wind?
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document.write( "Let \"u\" be the speed of the plane at no wind, 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  = 240 mph flying  with    the wind,\r\n" );
document.write( "and       effective speed is  = 180 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 = 240,    (1)\r\n" );
document.write( "u - v = 180.    (2)\r\n" );
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document.write( "To solve the system, add the two equations (both sides). You will get\r\n" );
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document.write( "2u = 240 + 180 = 420.   Hence,  u =  = 210.\r\n" );
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document.write( "Thus the speed of the plane at no wind is 210 miles per hour.\r\n" );
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document.write( "Next, from the equation (1) v = 240 - u = 240 - 210 = 30 miles per hour.\r\n" );
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document.write( "Thus the speed of the wind  is 30 miles per hour.\r\n" );
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document.write( "Answer.  The speed of the plane at no wind is 210 miles per hour.\r\n" );
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document.write( "         The speed of the wind  is 30 miles per hour.\r\n" );
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document.write( "Check.  The speed of the plane with the wind is 210 + 30 = 240 mph, and the flight time is  = 3 hours.\r\n" );
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document.write( "        The speed of the plane against the wind is 210 - 30 = 180 mph, and the flight time is  = 4 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
\n" ); document.write( "\"Word problems\", the topic \"Travel and Distance problems\".\r
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