document.write( "Question 992632: Justin recently drove to visit his parents who live 100 miles away. On his way there his average speed was 9 miles per hour faster than on his way home (he ran into some bad weather). If Justin spent a total of 5 hours driving, find the two rates. \n" ); document.write( "

Algebra.Com's Answer #612200 by stanbon(75887) $\"\"$ $\"About$

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Justin recently drove to visit his parents who live 100 miles away. On his way there his average speed was 9 miles per hour faster than on his way home (he ran into some bad weather). If Justin spent a total of 5 hours driving, find the two rates.
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\n" ); document.write( "Outward bound::
\n" ); document.write( "rate = x+9 ; dist = 100 m ; time = 100/(x+9) hrs
\n" ); document.write( "----
\n" ); document.write( "Homeward
\n" ); document.write( "rate = x mph ; dist = 100 m ; time = 100/x hrs
\n" ); document.write( "=======
\n" ); document.write( "Equation:
\n" ); document.write( "time + time = 5 hrs
\n" ); document.write( "100/(x+9) + 100/x = 5 hrs
\n" ); document.write( "----
\n" ); document.write( "100x + 100(x+9) = 5x(x+9)
\n" ); document.write( "----
\n" ); document.write( "200x + 900 = 5x^2 + 45x
\n" ); document.write( "5x^2 - 155x - 900 = 0
\n" ); document.write( "-----
\n" ); document.write( "x^2 - 31x - 180 = 0
\n" ); document.write( "-----
\n" ); document.write( "x = 36 mph
\n" ); document.write( "x+9 = 45 mph
\n" ); document.write( "------
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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