document.write( "Question 108296: At 10:00 A.M. a car leaves a house at a rate of 60mi/h. At the same time another car leaves the same house at a rate of 50mi/h in the opposite direction. At what time will the cars be 330 miles apart? \n" ); document.write( "

Algebra.Com's Answer #78912 by wgunther(43) $\"\"$ $\"About$

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if you draw a picture you get a better idea. Call the first car Car A and the second Car B. Car A is moving 60mi/h from the house, and Car B is moving 50mi/h from the house the other direction. \r
\n" ); document.write( "\n" ); document.write( "So, we can come up with 2 equations, one to describe each Car. Define Car A's motion to be positive, which means Car B's is negative as it's in the opposite direction.
\n" ); document.write( " $\"%0D%0Aa=60t%0D%0A\"$
\n" ); document.write( " $\"%0D%0Ab=-50t%0D%0A\"$
\n" ); document.write( "so, we want to find when the distance between the two is 330. Distance is the absolute value of the difference.
\n" ); document.write( " $\"%0D%0Aabs%28a-b%29=abs%2860t-%28-50t%29%29=abs%28110t%29=110t%0D%0A\"$
\n" ); document.write( "The absolute value drop as t must be positive (it's time). Then, we're looking when this distance is 330
\n" ); document.write( " $\"%0D%0A110t=330%0D%0At=3%0D%0A\"$
\n" ); document.write( "So the answer is 3 hours. \n" ); document.write( "

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