document.write( "Question 153517: Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle. \n" ); document.write( "

Algebra.Com's Answer #113046 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.
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\n" ); document.write( "Let s = his speed
\n" ); document.write( "then
\n" ); document.write( "(s+10) = the faster speed
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\n" ); document.write( "Write a time equation: Time = $\"dist%2Fspeed\"$
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\n" ); document.write( "Actual time = Faster time - 1 hr
\n" ); document.write( " $\"200%2Fs\"$ = $\"200%2F%28%28s%2B10%29%29\"$ + 1
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\n" ); document.write( "Multiply equation by common denominator, s(s+10); results:
\n" ); document.write( "200(s+10) = 200s + s(s+10)
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\n" ); document.write( "200s + 2000 = 200s + s^2 + 10s
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\n" ); document.write( "The 200s's are eliminated, leaving us with the quadratic equation:
\n" ); document.write( "s^2 + 10x - 2000 = 0
\n" ); document.write( "easily factors to:
\n" ); document.write( "(s+50)(s-40) = 0
\n" ); document.write( "Positive solution
\n" ); document.write( "s = 40 mph his speed
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\n" ); document.write( "Check solution by finding the time of each
\n" ); document.write( "200/40 = 5 hrs
\n" ); document.write( "200/50 = 4 hrs \n" ); document.write( "

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