document.write( "Question 160148: A man drives 108 km at an average rate. If he had driven 5 km/hr. faster, he would have made the trip in 15 hours less time. How fast did he drive? \n" ); document.write( "

Algebra.Com's Answer #118126 by ptaylor(2198) $\"\"$ $\"About$

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Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r\r
\n" ); document.write( "\n" ); document.write( "Let r=his rate over the 108 km
\n" ); document.write( "And r+5=his rate if he had driven 5 km/hr faster\r
\n" ); document.write( "\n" ); document.write( "Time it takes at the rate of r=108/r
\n" ); document.write( "Time it takes him at the rate of r+5=108/(r+5)\r
\n" ); document.write( "\n" ); document.write( "Now we are told that (108/r)-15=108/(r+5) multiply each term by r(r+5)
\n" ); document.write( "108(r+5)-15r(r+5)=108r get rid of parens and simplify
\n" ); document.write( "108r+540-15r^2-75r=108r subtract 108r from each side\r
\n" ); document.write( "\n" ); document.write( "108r-108r+540-15r^2-75r=108r-108r collect like terms
\n" ); document.write( "-15r^2-75r+540=0 divide each term by -15
\n" ); document.write( "r^2+5r-36=0 ----quadratic in standard form and it can be factored\r
\n" ); document.write( "\n" ); document.write( "(r+9)(r-4)=0
\n" ); document.write( "r+9=0
\n" ); document.write( "r=-9-------discount negative value for r
\n" ); document.write( "and
\n" ); document.write( "r-4=0
\n" ); document.write( "r=4 km/hr----------------------ans
\n" ); document.write( "CK
\n" ); document.write( "108/4 -15=108/9
\n" ); document.write( "27-15=12
\n" ); document.write( "12=12\r
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor\r
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