document.write( "Question 876953: An airplane flies 1449 mi against the wind
\n" ); document.write( "and 1539 mi with the wind in a total time of 5 hr. The
\n" ); document.write( "speed of the airplane in still air is 600 mph. What is the speed of the wind? \n" ); document.write( "

Algebra.Com's Answer #529063 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+w+\"$ = the windspeed in mi/hr
\n" ); document.write( " $\"+600+%2B+w+\"$ = the speed of the plane
\n" ); document.write( "flying with the wind
\n" ); document.write( " $\"+600+-+w+\"$ = the speed if the wind
\n" ); document.write( "flying against the wind
\n" ); document.write( "------------------------
\n" ); document.write( "(1) $\"+1449+=+%28+600+-+w+%29%2At%5B1%5D+\"$
\n" ); document.write( "(2) $\"+1539+=+%28+600+%2B+w+%29%2At%5B2%5D+\"$
\n" ); document.write( "(3) $\"+t%5B1%5D+%2B+t%5B2%5D+=+5+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "There are 3 equations and 3 unknowns
\n" ); document.write( "so it's solvable
\n" ); document.write( "(1) $\"+t%5B1%5D+=+1449+%2F+%28+600+-+w+%29+\"$
\n" ); document.write( "(2) $\"+t%5B2%5D+=+1539+%2F+%28+600+%2B+w+%29+\"$
\n" ); document.write( "------------------------------
\n" ); document.write( "By substitution:
\n" ); document.write( "(3) $\"+1449+%2F+%28+600+-+w+%29++%2B+1539+%2F+%28+600+%2B+w+%29+=+5+\"$
\n" ); document.write( "Multiply both sides by $\"+%28+600+-+w+%29%2A%28+600+%2B+w+%29+\"$
\n" ); document.write( "(3) $\"+1449%2A%28+600+%2B+w+%29+%2B+1539%2A%28+600+-+w+%29+=+5%2A%28+360000+-+w%5E2+%29+\"$
\n" ); document.write( "(3) $\"+869400+%2B+1449w+%2B+923400+-+1539w+=+1800000+-+5w%5E2+\"$
\n" ); document.write( "(3) $\"+5w%5E2+%2B+2988w+%2B+1792800+-+1800000+=+0+\"$
\n" ); document.write( "(3) $\"+5w%5E2+-+90w+-+7200+=+0+\"$
\n" ); document.write( "(3) $\"+w%5E2+-+18w+-+1440+=+0+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "I'll try completing the square:
\n" ); document.write( "(3) $\"+w%5E2+-+18w+%2B+%28+18%2F2+%29%5E2+=+1440+%2B+%28+18%2F2+%29%5E2+\"$
\n" ); document.write( "(3) $\"+w%5E2+-+18w+%2B+81+=+1440+%2B+81+\"$
\n" ); document.write( "(3) $\"+%28+w+-+9+%29%5E2+=+1521+\"$
\n" ); document.write( "(3) $\"+%28+w+-+9+%29%5E2+=+39%5E2+\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( "(3) $\"+w+-+9+=+39+\"$
\n" ); document.write( "(3) $\"+w+=+48+\"$
\n" ); document.write( "The windspeed is 48 mi/hr
\n" ); document.write( "-------------------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+1449+=+%28+600+-+48+%29%2At%5B1%5D+\"$
\n" ); document.write( "(1) $\"+t%5B1%5D+=+1449+%2F+552+\"$
\n" ); document.write( "(1) $\"+t%5B1%5D+=+2.625+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+t%5B2%5D+=+1539+%2F+%28+600+%2B+48+%29+\"$
\n" ); document.write( "(2) $\"+t%5B2%5D+=+1539+%2F+648+\"$
\n" ); document.write( "(2) $\"+t%5B2%5D+=+2.375+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+t%5B1%5D+%2B+t%5B2%5D+=+5+\"$
\n" ); document.write( "(3) $\"+2.625+%2B+2.375+=+5+\"$
\n" ); document.write( "(3) $\"+5+=+5+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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