document.write( "Question 172465: 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 #127381 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
\n" ); document.write( " would have taken 1 hour less. Find the speed of his vehicle.
\n" ); document.write( ":
\n" ); document.write( "Let s = original speed of the vehicle
\n" ); document.write( "then
\n" ); document.write( "(s+10) = the faster speed
\n" ); document.write( ":
\n" ); document.write( "Write a time equation, time = $\"dist%2Fspeed\"$
\n" ); document.write( ":
\n" ); document.write( "original time = faster time + 1 hour
\n" ); document.write( " $\"200%2Fs\"$ = $\"200%2F%28%28s%2B10%29%29\"$ + 1
\n" ); document.write( ":
\n" ); document.write( "Multiply equation by s(s+10)
\n" ); document.write( "s(s+10)* $\"200%2Fs\"$ = s(s+10)* $\"200%2F%28%28s%2B10%29%29\"$ + s(s+10)
\n" ); document.write( "Results:
\n" ); document.write( "200(s+10) = 200s + s^2 + 10s
\n" ); document.write( ":
\n" ); document.write( "200s + 2000 = 200s + s^2 + 10s
\n" ); document.write( ":
\n" ); document.write( "Arrange as quadratic equation:
\n" ); document.write( "s^2 + 10s + 200s - 200s - 2000 = 0
\n" ); document.write( ":
\n" ); document.write( "s^2 + 10s - 2000 = 0
\n" ); document.write( "Factors to:
\n" ); document.write( "(s + 50)(x - 40) = 0
\n" ); document.write( ":
\n" ); document.write( "s = + 40 mph is the original speed
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution by finding the times
\n" ); document.write( "200/40 = 5 hrs
\n" ); document.write( "200/50 = 4 hrs \n" ); document.write( "

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