document.write( "Question 1179659: Flying with the wind, a plane flew 1,120 mi in 4 h. Against the wind, the plane required 7 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 #853768 by n2(54) $\"\"$ $\"About$

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\n" ); document.write( "Flying with the wind, a plane flew 1,120 mi in 4 h.
\n" ); document.write( "Against the wind, the plane required 7 h to fly the same distance.
\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 u be the rate of the plane at no wind (in miles per hour)\r\n" );
document.write( "and v be the rate of the wind (in the same units).\r\n" );
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document.write( "Then the effective rate  of the plane with   the wind is u + v\r\n" );
document.write( "and  the effective rate of the plane against the wind is u - v.\r\n" );
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document.write( "From the problem, the effective rate of the plane with the wind is the distance of 1120 miles \r\n" );
document.write( "divided by the time of 4 hours  {{1120/4}}} = 280 mph.\r\n" );
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document.write( "                  The effective rate of the plane against the wind is the distance of 1120 miles \r\n" );
document.write( "divided by the time of 7 hours   = 160 mph.\r\n" );
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document.write( "So, we have two equations to find 'u' and 'v'\r\n" );
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document.write( "    u + v = 280,    (1)\r\n" );
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document.write( "    u - v = 160.    (2)\r\n" );
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document.write( "To solve, add equations (1) and (2).  The terms 'v' and '-v' will cancel each other, and you will get\r\n" );
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document.write( "    2u = 280 + 160 = 440  --->   u = 440/2 = 220.\r\n" );
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document.write( "Now from equation (1)\r\n" );
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document.write( "     v = 280 - u = 280 - 220 = 60.\r\n" );
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document.write( "ANSWER.  The rate of the plane in still air is 220 mph.  The rate of the wind is 60 mph km/h.\r\n" );
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