document.write( "Question 62053: Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour than Smith, and his trip took 1/2 hour longer than Smith's. How fast was each one traveling? \n" ); document.write( "
Algebra.Com's Answer #42806 by uma(370)\"\" \"About 
You can put this solution on YOUR website!
Let the speed of Smith be x mph\r
\n" ); document.write( "\n" ); document.write( "Then speed of Jones = (x+5) mph\r
\n" ); document.write( "\n" ); document.write( "Distance covered by Smith = 45 miles.\r
\n" ); document.write( "\n" ); document.write( "So time taken by Smith = Distance/time
\n" ); document.write( " = 45/x hrs\r
\n" ); document.write( "\n" ); document.write( "Distance covered by Jones = 70 miles.
\n" ); document.write( "Time taken by Jones = 70/(x+5) hrs.\r
\n" ); document.write( "\n" ); document.write( "By the given data,\r
\n" ); document.write( "\n" ); document.write( "70/(x+5) - 45/x = 1/2\r
\n" ); document.write( "\n" ); document.write( "Multiplying throughout by 2x(x+5) we get,
\n" ); document.write( "70*2x - 45*2(x+5) = x(x+5)\r
\n" ); document.write( "\n" ); document.write( "==> 140x - 90x - 450 = x^2 + 5x
\n" ); document.write( "==>50x - 450 - x^2 - 5x = 0
\n" ); document.write( "==> -x^2 + 45x - 450 = 0
\n" ); document.write( "==> x^2 - 45x + 450 = 0\r
\n" ); document.write( "\n" ); document.write( "==> x^2 - 15x - 30x + 450 = 0
\n" ); document.write( "==> x(x-15) - 30(x - 15) = 0
\n" ); document.write( "==> (x-15)(x-30) = 0
\n" ); document.write( "==> x-15 = 0 or x-30 = 0
\n" ); document.write( "==> x = 15 or x = 30\r
\n" ); document.write( "\n" ); document.write( "So either their speeds are 15 mph and 20 mph Or
\n" ); document.write( " their speeds are 30 mph and 35 mph respectively.
\n" ); document.write( "In either cases the difference in time taken = 1/2 hr.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Good Luck!!!
\n" ); document.write( " \n" ); document.write( "
\n" );