document.write( "Question 1177337: When a plane flies with the wind, it can travel 920 miles in 2 hours. When the plane flies in the opposite direction, against the wind, it takes 4 hours to fly the same distance. Find the rate of the plane in still air and the rate of the wind. \n" ); document.write( "

Algebra.Com's Answer #853738 by ikleyn(53646) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "When a plane flies with the wind, it can travel 920 miles in 2 hours.
\n" ); document.write( "When the plane flies in the opposite direction, against the wind, it takes 4 hours to fly the same distance.
\n" ); document.write( "Find the rate of the plane in still 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 920 miles \r\n" );
document.write( "divided by the time of 2 hours   = 460 mph.\r\n" );
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document.write( "                  The effective rate of the plane against the wind is the distance of 920 miles \r\n" );
document.write( "divided by the time of 4 hours   = 230 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 = 460,    (1)\r\n" );
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document.write( "    u - v = 230.    (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 = 460 + 230 = 690  --->   u = 690/2 = 345.\r\n" );
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document.write( "Now from equation (1)\r\n" );
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document.write( "     v = 460 - u = 460 - 345 = 115.\r\n" );
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document.write( "ANSWER.  The rate of the plane in still air is 345 mph.  The rate of the wind is 115 mph km/h.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "This solution produces the same answer as in the post by @mananth, but has an advantage
\n" ); document.write( "that it does not contain excessive calculations that the solution by @mananth has.\r
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\n" ); document.write( "\n" ); document.write( "We, the tutors, write here our solutions not only to get certain numerical answer.
\n" ); document.write( "We write to teach - and, in particular, to teach solving in a right style.\r
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\n" ); document.write( "\n" ); document.write( "This style solving presented in my post, is straightforward with no logical loops.
\n" ); document.write( "The solution presented in the post by @mananth has two logical loops.\r
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document.write( "    One loop in the @mananth post is writing\r\n" );
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document.write( "        d/r = t  --->  920/(x+y) = 2   --->   2x + 2y = 920  --->  /2  --->  x+y = 460,\r\n" );
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document.write( "    while in my solution I simply write for the effective rate \r\n" );
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document.write( "        u + v = 920/2 = 460.\r\n" );
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document.write( "    Second loop in the @mananth post is writing\r\n" );
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document.write( "                       920/(x-y) = 4   --->   4x - 4y = 920  --->  /4  --->  x-y = 230,\r\n" );
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document.write( "    while in my solution I simply write for the effective rate upstream\r\n" );
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document.write( "        u - v = 920/4 = 230.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is why I presented my solution here and why I think it is better than the solution by @mananth:
\n" ); document.write( "- because it teaches students to present their arguments in a straightforward way, without logical zigzags.\r
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\n" ); document.write( "\n" ); document.write( "@mananth repeats his construction of solution with no change for all similar problems on flies
\n" ); document.write( "with and against the wind simply because his COMPUTER CODE is written this way.
\n" ); document.write( "But this way is not pedagogically optimal - in opposite, it is pedagogically imperfect.\r
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