document.write( "Question 1058812: An airplane takes 3
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\n" ); document.write( "hours against the wind. Find the speed of the plane in still air and the speed of the wind.\r
\n" ); document.write( "\n" ); document.write( "I had a question about how would I have to set up this problem in order to find both my speeds? I have been stuck on this question for hours please, help! \n" ); document.write( "

Algebra.Com's Answer #673921 by ikleyn(52777) $\"\"$ $\"About$

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\n" ); document.write( "An airplane takes 3 hours to travel a distance of 1800 miles with the wind. The return trip takes 4 hours against the wind.
\n" ); document.write( "Find the speed of the plane in still air and the speed of the wind.\r
\n" ); document.write( "\n" ); document.write( "I had a question about how would I have to set up this problem in order to find both my speeds?
\n" ); document.write( "I have been stuck on this question for hours please, help!
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document.write( " = u + v   (1)  is the equation for the flight with the wind.\r\n" );
document.write( "                      (Here \"u\" is the airspeed of the airplane with NO wind,\r\n" );
document.write( "                            \"v\" is the wind speed)\r\n" );
document.write( " = u - v   (2)  is the equation for the flight against the wind.\r\n" );
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document.write( "Simplify equations (1) and (2) and write them as a system:\r\n" );
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document.write( "u + v = 600,           (1')\r\n" );
document.write( "u - v = 450.           (2')\r\n" );
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document.write( "Now add the two equations (1') and (2'). You will get\r\n" );
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document.write( "2u = 1050  --->  u =  = 525 miles per hour.\r\n" );
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document.write( "Having this, you can easily determine \"v\" from (1'):  \r\n" );
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document.write( "v = 600 - 525 = 75 miles per hour.\r\n" );
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document.write( "Answer.  The plane airspeed  is 525 mph. The wind speed is 75 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
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\n" ); document.write( "\n" ); document.write( "You will find the detailed solutions of many similar problems there. \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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