document.write( "Question 164638This question is from textbook
\n" ); document.write( ": Steve traveled 200 miles at a certain speeed. 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 #121340 by ptaylor(2198)\"\" \"About 
You can put this solution on YOUR website!
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 speed of Steve's vehicle
\n" ); document.write( "Let t=time required to travel 200 mi at this certain speed, so:
\n" ); document.write( "t=200/r --------------------eq1
\n" ); document.write( "Now we are also told that:
\n" ); document.write( "t-1=200/(r+10)--------------------eq2
\n" ); document.write( "substitute t=200/r from eq1 into eq2 and we get:\r
\n" ); document.write( "\n" ); document.write( "(200/r)-1=200/(r+10) multiply each term by r(r+10)
\n" ); document.write( "200(r+10)-r(r+10)=200r get rid of parens (distributive)
\n" ); document.write( "200r+2000-r^2-10r=200r subtract 200r from each side
\n" ); document.write( "200r-200r+2000-r^2-10r=200r-200r collect like terms
\n" ); document.write( "-r^2-10r+2000=0 multiplpy each term by -1
\n" ); document.write( "r^2+10r-2000=0--Quadratic in standard form and it can be factored
\n" ); document.write( "(r+50)(r-40)=0
\n" ); document.write( "r+50=0
\n" ); document.write( "r=-50-------------------disregard negative value for r; rates are positive in this problem
\n" ); document.write( "and
\n" ); document.write( "r-40=0
\n" ); document.write( "r=40 mph------------speed of Steve's vehicle
\n" ); document.write( "CK
\n" ); document.write( "200/40=5 hrs
\n" ); document.write( "200/50=4 hrs\r
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor
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