document.write( "Question 122155This question is from textbook algebra: structure and Method: book 1
\n" ); document.write( ": If I increase my usual driving speed by 10 km/h, I can drive the 255 km trip to Nashville in 24 min less than usual. How fast do I usually drive? PLEASE HELP!!!! There is not an answer in the back, and I also don't know what to do!!!!HELP!!!!!!!!!!!!!!!!!!! I am sorry if this is not enough info, but that is all there is in the book. \n" ); document.write( "
Algebra.Com's Answer #89866 by solver91311(24713)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "First note that 24 minutes is 0.4 hour.\r\n" );
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document.write( "Next, we know that the distance from home to Nashville doesn't change, so\r\n" );
document.write( "if the speed you generally travel is r, and we know that \"d=rt\", we can say\r\n" );
document.write( "that \"rt=255\".\r\n" );
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document.write( "We also know that 10 km/hr faster gets us there 0.4 hour sooner, so\r\n" );
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document.write( "\"%28r%2B10%29%28t-0.4%29=255\"\r\n" );
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document.write( "\"r=255%2Ft\" and\r\n" );
document.write( "\"r%2B10=255%2F%28t-0.4%29\" => \"r=%28255%2F%28t-0.4%29%29-10\"\r\n" );
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document.write( "Therefore \"255%2Ft=%28255%2F%28t-0.4%29%29-10\"\r\n" );
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document.write( "Put everything on the left:\r\n" );
document.write( "\"255%2Ft-%28255%2F%28t-0.4%29%29%2B10=0\"\r\n" );
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document.write( "Find the LCD.  Factors are t, (t-0.4), and 1.  So the LCD is t(t-0.4).\r\n" );
document.write( "Don't bother to multiply it out.  That won't help at this point.\r\n" );
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document.write( "Convert the three fractions to have the LCD:\r\n" );
document.write( "\"%28255%28t-0.4%29-255t%2B10t%28t-0.4%29%29%2Ft%28t-0.4%29=0\"\r\n" );
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document.write( "Simplify the numerator\r\n" );
document.write( "\"%28255t-102-255t%2B10t%5E2-4t%29%2Ft%28t-0.4%29=0\"\r\n" );
document.write( "\"%2810t%5E2-4t-102%29%2Ft%28t-0.4%29=0\"\r\n" );
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document.write( "Since \"a%2Fb=0\" if and only if \"a=0\" and \"b%3C%3E0\", we only have to\r\n" );
document.write( "solve for \"10t%5E2-4t-102=0\" and exclude any roots that make \"t%28t-0.4%29\"\r\n" );
document.write( "equal zero because you can't divide by zero.\r\n" );
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document.write( "I'll let you handle the work of solving the quadratic, but suffice it to say\r\n" );
document.write( "that the roots are 3.4 and -3.  Since we are solving for time, -3 can be\r\n" );
document.write( "excluded.  As much as we would like to be able to turn back the clock, negative\r\n" );
document.write( "time just doesn't make much sense.\r\n" );
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document.write( "Knowing that the normal time it takes to get there is 3.4 hours, you can easily\r\n" );
document.write( "calculate your normal rate, \"r=255%2F3.4=75\"  So your normal rate is 75 km/hr.\r\n" );
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document.write( "Just under 47 mph -- slowpoke!\r\n" );
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