document.write( "Question 132829: Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle \n" ); document.write( "

Algebra.Com's Answer #97134 by ptaylor(2198) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "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=the certain speed
\n" ); document.write( "And r+20=the 20 mph faster speed\r
\n" ); document.write( "\n" ); document.write( "Time required to go 600 mi at the certain speed=600/r
\n" ); document.write( "Time to go 600 mi at the faster speed=600/(r+20)\r
\n" ); document.write( "\n" ); document.write( "Now we are told that the time at this faster speed is one hour less than the time at the certain speed, so:\r
\n" ); document.write( "\n" ); document.write( "(600/r)-1=600/(r+20) multiply each term by r(r+20)
\n" ); document.write( "600(r+20)-r(r+20)=600r get rid of parens\r
\n" ); document.write( "\n" ); document.write( "600r+12000-r^2-20r=600r subtract 600r from each side\r
\n" ); document.write( "\n" ); document.write( "600r-600r+12000-r^2-20r=600r-600r collect like terms\r
\n" ); document.write( "\n" ); document.write( "-r^2-20r+12000=0 multiply each term by -1
\n" ); document.write( "r^2+20r-12000=0---------------------quadratic in standard form
\n" ); document.write( "Solve using the quadratic formula
\n" ); document.write( " $\"r=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"r+=+%28-20+%2B-+sqrt%28+400%2B48000+%29%29%2F%282%29+\"$
\n" ); document.write( " $\"r+=+%28-20+%2B-+sqrt%28+52000+%29%29%2F%282%29+\"$
\n" ); document.write( " $\"r+=+%28-20+%2B-228.035%29%2F%282%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Disregard the negative value for r. In this case speed is positive\r
\n" ); document.write( "\n" ); document.write( " $\"r+=+%28-20+%2B228.035%29%2F%282%29+\"$
\n" ); document.write( " $\"r+=+%28-20+%2B228.035%29%2F%282%29+\"$
\n" ); document.write( "r=~~~~~~~104 mph\r
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\n" ); document.write( "\n" ); document.write( "CK
\n" ); document.write( "Time at 104 mph=600/104=5.769 ~~~~~~5.8 hrs
\n" ); document.write( "Time at 104+20=600/124=4.8387 ~~~~~~~4.8 hrs\r
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\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor\r
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