document.write( "Question 1179658: A plane traveling with the wind flew 1312.5 mi in 5.25 h. Against the wind, the plane required 6.25 h to fly the same distance. Find the rate of the plane in calm air and the rate of the wind. \n" ); document.write( "

Algebra.Com's Answer #853755 by n2(54) $\"\"$ $\"About$

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\n" ); document.write( "A plane traveling with the wind flew 1312.5 mi in 5.25 h.
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\n" ); document.write( "Find the rate of the plane in calm air and the rate of the wind.
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document.write( "Let x be the rate of the plane in calm air, in miles per hour.\r\n" );
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document.write( "Let y be the rate of the wind.\r\n" );
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document.write( "Then  the effective speed of the plane with    the wind is (x+y) mph,\r\n" );
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document.write( "while the effective speed of the plane against the wind is (x-y) mph,\r\n" );
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document.write( "From the problem, the effective rate of the plane with the wind is  the distance divided by the travel time\r\n" );
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document.write( "     = 250 miles per hour,\r\n" );
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document.write( "and the effective rate of the plane against the wind is  the distance divided by the travel time\r\n" );
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document.write( "     = 210 miles per hour.\r\n" );
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document.write( "So, we have these two equations\r\n" );
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document.write( "    x + y = 250     (1)\r\n" );
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document.write( "    x - y = 210     (2)\r\n" );
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document.write( "To find x, add the equation.  You will get\r\n" );
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document.write( "    2x = 250 + 210 = 460,  x = 460/2 = 230.\r\n" );
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document.write( "Now express y from equation (1) and calculate\r\n" );
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document.write( "    y = 250 - x = 250 - 230 = 20.\r\n" );
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document.write( "At this point the problem is solved completely.\r\n" );
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document.write( "ANSWER.  The speed of the plane in calm air is 230 mph.  The rate of the wind is 20 mph.\r\n" );
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