document.write( "Question 1159145: Cabrina and Dabney are attending a conference. After the conference, Cabrina drives home to Boise at an average speed of 55 miles per hour and Dabney drives home to Portland at an average speed of 40 miles per hour. If the sum of their driving times is 11.9 hours and if the sum of the distances driven is 566 miles, determine the time each woman spent driving home. \n" ); document.write( "

Algebra.Com's Answer #782143 by Shin123(626) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let's say that Cabrina spent x hours driving home and Dabney spent y hours driving home. We have the equations:
$\"system%28x%2By=11.9%2C55x%2B40y=566%29\"$
Multiplying the first equation by 40 gives $\"system%2840x%2B40y=476%2C55x%2B40y=566%29\"$ Subtracting the first equation from the second gives $\"15x=90\"$ . Dividing both sides by 15 gives $\"highlight%28highlight_green%28highlight%28x=6%29%29%29\"$ . Plugging this value into the second equation gives $\"highlight%28highlight_green%28highlight%28y=5.9%29%29%29\"$ . So Cabrina drove for 6 hours and Dabney drove for 5.9 hours. \n" ); document.write( "

\n" );