document.write( "Question 1192602: In going over 750 kms, it takes a passenger plane 2 hour less time to fly with a tailwind of 50 kph than against a headwind travelling at the same speed. How fast was the passenger plane flying at each way of the course? \n" ); document.write( "
Algebra.Com's Answer #824482 by math_helper(2461)\"\" \"About 
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\n" ); document.write( "With the tailwind: \"v%5B1%5D++=+750%2Ft%5B1%5D+\" (1)\r
\n" ); document.write( "\n" ); document.write( "With the headwind: \"v%5B2%5D+=+750%2Ft%5B2%5D+\" (2)\r
\n" ); document.write( "\n" ); document.write( "Also, from the problem statement:
\n" ); document.write( " \"+t%5B1%5D+=+t%5B2%5D+-+2+\" or \"t%5B2%5D+=+t%5B1%5D+%2B+2+\" (3)
\n" ); document.write( " \"+v%5B1%5D+-+50+=+v%5B2%5D+%2B+50+\" (4)\r
\n" ); document.write( "\n" ); document.write( "With this information, you can write an equation with one unknown. I chose to write it with just \"t%5B1%5D\" but other elimination possibilities exist:\r
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\n" ); document.write( "\n" ); document.write( "Multiply both sides by \"t%5B1%5D%28t%5B1%5D%2B2%29+\":
\n" ); document.write( " \"+750%28t%5B1%5D%2B2%29+=+750t%5B1%5D+%2B+100%28t%5B1%5D%29%28t%5B1%5D%2B2%29+\"\r
\n" ); document.write( "\n" ); document.write( "Simplify...
\n" ); document.write( " \"+750t%5B1%5D+%2B+1500+=+750t%5B1%5D+%2B+100t%5B1%5D%5E2+%2B+200t%5B1%5D+\"
\n" ); document.write( " \"+100t%5B1%5D%5E2+%2B+200t%5B1%5D+-+1500+=+0+\"
\n" ); document.write( " \"++t%5B1%5D%5E2+%2B+2t%5B1%5D+-+15+=+0+\"\r
\n" ); document.write( "\n" ); document.write( "Factor:
\n" ); document.write( " \"+%28t%5B1%5D-3%29%28t%5B1%5D%2B5%29+=+0+\"\r
\n" ); document.write( "\n" ); document.write( "This has solutions \"t%5B1%5D+=+3+\" and \"t%5B1%5D=-5\"\r
\n" ); document.write( "\n" ); document.write( "Take just the positive time solution \"+t%5B1%5D+=+3+\" --(by 3)--> \"+t%5B2%5D+=+5+\"\r
\n" ); document.write( "\n" ); document.write( "Now, \"highlight%28+v%5B1%5D+=+750%2F3+=+250+%29+\" km/hr
\n" ); document.write( " \"highlight%28+v%5B2%5D+=+750%2F5+=+150+%29+\" km/hr\r
\n" ); document.write( "\n" ); document.write( "Check: \"v%5B1%5D+-+v%5B2%5D+=+100+\" --> \"v%5B1%5D+-+50+=+v%5B2%5D+%2B+50+\" (ok)\r
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