Algebra.Com's Answer #793702 by ikleyn(52780)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
.
\n" );
document.write( "You commute to work at a distance of 40 miles and return on the same route at the end of the day.
\n" );
document.write( "Your average speed on the return trip is 30 miles per hour faster than your average speed on the morning’s outgoing trip.
\n" );
document.write( "If the round trip takes 2 hours, what are your average speeds each way? Define each variable(s).
\n" );
document.write( "~~~~~~~~~~~~~~~\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "\r\n" );
document.write( "Let x be the rate commuting to work (in miles per hour).\r\n" );
document.write( "\r\n" );
document.write( "Then the rate commuting back is (x+30) mph.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The time commuting to work is  hours.\r\n" );
document.write( "\r\n" );
document.write( "The time commuting back is  hours.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The total time commuting to work and back is 2 hours, which gives you the \"time\" equation\r\n" );
document.write( "\r\n" );
document.write( " + = 2 hours. (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is your basic equation. The setup is just completed.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To solve the equation, multiply both sides by x*(x+30). You will get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " 40*(x+30) + 40x = 2*x*(x+30).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " 40x + 1200 + 40x = 2x^2 + 60x\r\n" );
document.write( "\r\n" );
document.write( " 2x^2 - 20x - 1200 = 0\r\n" );
document.write( "\r\n" );
document.write( " x^2 - 10x - 600 = 0\r\n" );
document.write( "\r\n" );
document.write( "Factor left side\r\n" );
document.write( "\r\n" );
document.write( " (x-30)*(x+20) = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Of the two roots, x= 30 and x= -20, only positive root x= 30 makes sense.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, the ANSWER is: the rate commuting to work is 30 mph; the rate commuting back is 30+30 = 60 mph.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK. I will check if the equation (1) is valid:  +  =  +  = 2. ! Correct !\r\n" );
document.write( " \r
\n" );
document.write( "\n" );
document.write( "The problem is just solved.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "-------------\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "The method of solution is using the \"time\" equation.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "MEMORIZE this method (!)\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( " |