document.write( "Question 575446: Please help me solve this word problem. I know the basic formula is rt=d but i don't know how to apply the words to the formula to solve.
\n" ); document.write( "Joe flew 300 miles with the wind in two hours. After flying against the wind for two hours, he made 270 miles of the return trip. Find the wind speed and the speed of the plane in still air. \n" ); document.write( "
Algebra.Com's Answer #369477 by Edwin McCravy(20062)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You are asked for two speeds.  But actually there are four speeds to\r\n" );
document.write( "consider:\r\n" );
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document.write( "1.  The speed at which the plane would be traveling if there was no wind,\r\n" );
document.write( "    (which is not the case).   Let's call this speed x\r\n" );
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document.write( "2.  The speed of the wind.  Let's call this speed w.\r\n" );
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document.write( "3.  The faster speed with the wind.  This is the actual faster speed of the\r\n" );
document.write( "    plane when the wind is blowing in the direction the plane is flying.  This\r\n" );
document.write( "    speed is x+w.\r\n" );
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document.write( "4.  The slower speed against the wind.  This is the actual slower speed of the\r\n" );
document.write( "    plane when the wind is blowing in the opposite direction to the direction\r\n" );
document.write( "    the plane is flying.  This speed is x+w.\r\n" );
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\n" ); document.write( "Joe flew 300 miles with the wind in two hours.
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document.write( "So we use the formula rt = d substituting (x+w) for r, 2 for t, and 300 for d:\r\n" );
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document.write( "                      rt = d\r\n" );
document.write( "                  (x+w)2 = 300\r\n" );
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document.write( "We divide both sides by 2:\r\n" );
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document.write( "                     x+w = 150\r\n" );
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\n" ); document.write( "After flying against the wind for two hours, he made 270 miles of the return trip.
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document.write( "So we use the formula rt = d again but this time substituting (x-w) for r, \r\n" );
document.write( "2 again for t, but only 270 for d:\r\n" );
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document.write( "                      rt = d\r\n" );
document.write( "                  (x-w)2 = 270\r\n" );
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document.write( "We divide both sides by 2:\r\n" );
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document.write( "                     x-w = 135\r\n" );
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document.write( "So we have this system of equations to solve:\r\n" );
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document.write( "                     x+w = 150\r\n" );
document.write( "                     x-w = 135\r\n" );
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document.write( "Solve that system and get x = 142.5 mph and w = 7.5 mph\r\n" );
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document.write( "The wind speed is 7.5 mph and the speed of the plane in still air is 142.5 mph.\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "With the wind the plane was traveling 142.5+7.5 or 150mph, and in 2 hours\r\n" );
document.write( "he traveled twice 150 or 300 miles.  That checks.\r\n" );
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document.write( "And against the wind the plane was traveling 142.5-7.5 or 135mph, and in \r\n" );
document.write( "2 hours he traveled twice 135 or 270 miles.  That checks. So we know the \r\n" );
document.write( "answers are correct.\r\n" );
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document.write( "Edwin
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