document.write( "Question 96020: During rush hour, Ella can drive 60 miles using the side roads in the same time that it takes to travel 25 miles on the freeway. If Ella's rate on the side roads is 7 mi/h faster than her rate on the freeway, find her rate on the side roads. \n" ); document.write( "

Algebra.Com's Answer #69923 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
During rush hour, Ella can drive 60 miles using the side roads in the same time that it takes to travel 25 miles on the freeway. If Ella's rate on the side roads is 7 mi/h faster than her rate on the freeway, find her rate on the side roads.
\n" ); document.write( "

\r\n" );
document.write( "This problem sounds odd because you normally would\r\n" );
document.write( "think of being able to drive faster on freeways than\r\n" );
document.write( "on side roads, but this problem has her driving\r\n" );
document.write( "faster on the side roads.  Oh well, maybe it's\r\n" );
document.write( "bumper-to-bumper on the freeway at rush hour. \r\n" );
document.write( "\r\n" );
document.write( "Make this chart.\r\n" );
document.write( "\r\n" );
document.write( "                   Distance   Rate     Time\r\n" );
document.write( " On side roads      \r\n" );
document.write( " On freeway \r\n" );
document.write( "\r\n" );
document.write( "Let x = her rate on the freeway, so fill in x\r\n" );
document.write( "for the rate on the freeway:\r\n" );
document.write( "\r\n" );
document.write( "                   Distance   Rate     Time\r\n" );
document.write( " On side roads           \r\n" );
document.write( " On freeway                     x      \r\n" );
document.write( "\r\n" );
document.write( ">>...60 miles using the side roads...<<\r\n" );
document.write( "\r\n" );
document.write( "So fill in 60 for her distance using the side roads\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                   Distance   Rate     Time\r\n" );
document.write( " On side roads        60       \r\n" );
document.write( " On freeway                     x      \r\n" );
document.write( "\r\n" );
document.write( ">>...25 miles on the freeway...<<\r\n" );
document.write( "\r\n" );
document.write( "So fill in 25 for her distance using the freeway\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                   Distance   Rate     Time\r\n" );
document.write( " On side roads        60              \r\n" );
document.write( " On freeway           25        x     \r\n" );
document.write( "\r\n" );
document.write( ">>...Ella's rate on the side roads is 7 mi/h faster than \r\n" );
document.write( "her rate on the freeway...<<\r\n" );
document.write( "\r\n" );
document.write( "So add 7 to x, her rate on the freeway, to get x+7 and fill\r\n" );
document.write( "that in for he rate on the side roads. \r\n" );
document.write( "\r\n" );
document.write( "                   Distance   Rate     Time\r\n" );
document.write( " On side roads        60       x+7       \r\n" );
document.write( " On freeway           25        x  \r\n" );
document.write( "\r\n" );
document.write( "Next use Time = Distance/Rate to fill in both times:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                   Distance   Rate     Time\r\n" );
document.write( " On side roads        60       x+7    60/(x+7)\r\n" );
document.write( " On freeway           25        x      25/x\r\n" );
document.write( "\r\n" );
document.write( "Now that the chart is filled in, we must make our equation.\r\n" );
document.write( "\r\n" );
document.write( ">>...Ella can drive 60 miles using the side roads in the same\r\n" );
document.write( "time that it takes to travel 25 miles on the freeway...<<\r\n" );
document.write( "\r\n" );
document.write( "The key words are \"same time\".  When things are the same, they are\r\n" );
document.write( "equal. So we set the two times equal.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "All you have to do now is solve for x.\r\n" );
document.write( "\r\n" );
document.write( "You get x = 5, so she traveled 5 mi/hr on the freeway. \r\n" );
document.write( "\r\n" );
document.write( "(Yes, it must be rush hour.  Why do they call it \r\n" );
document.write( "\"rush hour\" when nobody rushes at all?  :-)\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );