document.write( "Question 226232: An airplane travels 600 miles against the wind in 3.5 hours and makes the return trip (with the wind) in 2.5 hours. Find the rate of the wind \n" ); document.write( "

Algebra.Com's Answer #168531 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"s\"$ = rate of airplane
\n" ); document.write( "Let $\"w\"$ = rate of wind
\n" ); document.write( " $\"s+%2B+w\"$ = rate flying with the wind
\n" ); document.write( " $\"s+-+w\"$ = rate flying against the wind
\n" ); document.write( "given:
\n" ); document.write( " $\"t+=+2.5\"$ hrs with the wind
\n" ); document.write( " $\"t+=+3.5\"$ hrs against the wind
\n" ); document.write( " $\"d+=+600\"$ mi
\n" ); document.write( "---------------
\n" ); document.write( "I can now write equations
\n" ); document.write( " $\"600+=+%28s+%2B+w%29%2A2.5\"$
\n" ); document.write( " $\"600+=+%28s+-+w%29%2A3.5\"$
\n" ); document.write( "This is 2 equations and 2 unknowns, so it's solvable
\n" ); document.write( " $\"2.5s+%2B+2.5w+=+600\"$
\n" ); document.write( " $\"3.5s+-+3.5w+=+600\"$
\n" ); document.write( "Multiply both equations by $\"10\"$
\n" ); document.write( " $\"25s+%2B+25w+=+6000\"$
\n" ); document.write( " $\"35s+-+35w+=+6000\"$
\n" ); document.write( "Divide both equations by $\"5\"$
\n" ); document.write( " $\"5s+%2B+5w+=+1200\"$
\n" ); document.write( " $\"7s+-+7w+=+1200\"$
\n" ); document.write( "Multiply the 1st equation by $\"7\"$ and
\n" ); document.write( "the 2nd equation by $\"5\"$
\n" ); document.write( " $\"35s+%2B+35w+=+8400\"$
\n" ); document.write( " $\"35s+-+35w+=+6000\"$
\n" ); document.write( "Add the equations
\n" ); document.write( " $\"70s+=+14400\"$
\n" ); document.write( " $\"s+=+205.71\"$
\n" ); document.write( "and, since
\n" ); document.write( " $\"5s+%2B+5w+=+1200\"$
\n" ); document.write( " $\"5%2A205.71+%2B+5w+=+1200\"$
\n" ); document.write( " $\"5w+=+1200+-+1028.57\"$
\n" ); document.write( " $\"5w+=+171.429\"$
\n" ); document.write( " $\"w+=+34.29\"$
\n" ); document.write( "The wind speed is 34.29 mi/hr
\n" ); document.write( "check:
\n" ); document.write( " $\"600+=+%28s+%2B+w%29%2A2.5\"$
\n" ); document.write( " $\"600+=+%28205.71+%2B+34.29%29%2A2.5\"$
\n" ); document.write( " $\"600+=+239.996%2A2.5\"$
\n" ); document.write( " $\"600+=+599.989\"$ close enough
\n" ); document.write( "and
\n" ); document.write( " $\"600+=+%28s+-+w%29%2A3.5\"$
\n" ); document.write( " $\"600+=+%28205.71+-+34.29%29%2A3.5\"$
\n" ); document.write( " $\"600+=+171.42%2A3.5\"$
\n" ); document.write( " $\"600+=+599.97\"$ close enough
\n" ); document.write( " \n" ); document.write( "

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