document.write( "Question 117642: THE SPEED OF AN AIRPLANE IN STILL AIR IS 224KM/H. THE PLANE TRAVELS 733KM AGAINST THE WIND AND 1075KM WITH THE WIND IN A TOTAL TIME OF 15HR. WHAT IS THE SPEED OF THE WIND \n" ); document.write( "

Algebra.Com's Answer #85803 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
After a lot of tough calculations, I get $\"w+=+164.065\"$ for
\n" ); document.write( "the windspeed. Plugging it back into the formula, it seems
\n" ); document.write( "to check OK.
\n" ); document.write( "The formula I used is:
\n" ); document.write( " $\"%28733+%2F+%28224+-+w%29%29+%2B+%281075+%2F+%28224+%2B+w%29%29+=+15\"$
\n" ); document.write( "I multiply both sides by $\"224+-+w\"$
\n" ); document.write( " $\"733+%2B+1075%2A%28%28224-w%29%2F%28224%2Bw%29%29+=+15%28224-w%29\"$
\n" ); document.write( " $\"1075%2A%28%28224-w%29%2F%28224%2Bw%29%29+=+15%28224-w%29+-+733\"$
\n" ); document.write( " $\"1075%2A%28224-w%29+=+%28224%2Bw%29%2A%283360+-+15w+-733%29\"$
\n" ); document.write( " $\"240800+-+1075w+=+%28224%2Bw%29%282627+-+15w%29\"$
\n" ); document.write( " $\"240800+-+1075w+=+588448+%2B+2627w+-+3360w+-+15w%5E2\"$
\n" ); document.write( " $\"-15w%5E2+%2B+3702w+-3360w+-240800+%2B+588448+=+0\"$
\n" ); document.write( " $\"-15w%5E2+%2B+342w+%2B+347648\"$
\n" ); document.write( "Using the quadratic equation
\n" ); document.write( " $\"w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"w+=+%28-342+%2B-+sqrt%28+342%5E2-4%2A%28-15%29%2A347648+%29%29%2F%282%2A%28-15%29%29+\"$
\n" ); document.write( " $\"w+=+%28-342+%2B-+sqrt%28+116964+%2B+20858880%29%29+%2F+-30\"$
\n" ); document.write( " $\"w+=+%28-342+%2B-+sqrt%2820975844%29%29+%2F+-30\"$
\n" ); document.write( " $\"w+=+%28-342+%2B-+4579.9393%29+%2F+-30\"$
\n" ); document.write( "I want a positive result for the windspeed, so I must
\n" ); document.write( "have a negative result in the numerator because -/- = +
\n" ); document.write( " $\"w+=+%28-4921.93930%29+%2F+-30\"$
\n" ); document.write( " $\"w+=+164.0646\"$ mi/hr windspeed
\n" ); document.write( "check answer
\n" ); document.write( " $\"%28733+%2F+%28224+-+w%29%29+%2B+%281075+%2F+%28224+%2B+w%29%29+=+15\"$
\n" ); document.write( " $\"%28733+%2F+%28224+-+164.0646%29%29+%2B+%281075+%2F+%28224+%2B+164.0646%29%29+=+15\"$
\n" ); document.write( " $\"733+%2F+59.93536%29+%2B+%281075+%2F+388.0646%29+=+15\"$
\n" ); document.write( " $\"12.22984+%2B+2.770157+=+15\"$
\n" ); document.write( " $\"14.99999734+=+15\"$
\n" ); document.write( "close enough \n" ); document.write( "

\n" );