document.write( "Question 150817: A plane can travel 400 miles against the wind in the same time that it can travel 500 miles with the wind. If the speed of wind was 10 miles per hour. Find the speed of the plane in still air. \n" ); document.write( "

Algebra.Com's Answer #110856 by josmiceli(19441) $\"\"$ $\"About$

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Windspeed = $\"w\"$
\n" ); document.write( " $\"w+=+10+mi%2Fhr\"$
\n" ); document.write( " $\"p\"$ = speed of plane is still air
\n" ); document.write( " $\"t\"$ = time flying against and with the wind
\n" ); document.write( "Against the wind:
\n" ); document.write( "(1) $\"400+=+%28p+-+10%29%2At\"$
\n" ); document.write( "With the wind:
\n" ); document.write( "(2) $\"500+=+%28p+%2B+10%29%2At\"$
\n" ); document.write( "Multiply both sides of (1) by $\"5\"$
\n" ); document.write( "Multiply both sides of (2) by $\"4\"$
\n" ); document.write( " $\"2000+=+5%2A%28p+-+10%29%2At\"$
\n" ); document.write( "and
\n" ); document.write( " $\"2000+=+4%2A%28p+%2B+10%29%2At\"$
\n" ); document.write( "Since they both equal 2000, make them equal to eachother
\n" ); document.write( " $\"5%2A%28p+-+10%29%2At+=+4%2A%28p+%2B+10%29%2At\"$
\n" ); document.write( "Divide both sides by $\"t\"$
\n" ); document.write( " $\"5%2A%28p+-+10%29+=+4%2A%28p+%2B+10%29\"$
\n" ); document.write( " $\"5p+-+50+=+4p+%2B+40\"$
\n" ); document.write( " $\"p+=+90\"$ mi/hr
\n" ); document.write( "The speed of the plane in still air is 90 mi/hr
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"400+=+%28p+-+10%29%2At\"$
\n" ); document.write( "(1) $\"400+=+%2890+-+10%29%2At\"$
\n" ); document.write( " $\"400+=+80t\"$
\n" ); document.write( " $\"t+=+5\"$ hrs
\n" ); document.write( "and
\n" ); document.write( "(2) $\"500+=+%28p+%2B+10%29%2At\"$
\n" ); document.write( "(2) $\"500+=+%2890+%2B+10%29%2At\"$
\n" ); document.write( " $\"500+=+100t\"$
\n" ); document.write( " $\"t+=+5\"$ hrs
\n" ); document.write( "OK \n" ); document.write( "

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