document.write( "Question 114060: 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 #83169 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
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( ":
\n" ); document.write( "Let x = his actual speed
\n" ); document.write( "Then
\n" ); document.write( "(x+20) = the faster speed, that would have reduced the time by 1 hr
\n" ); document.write( ":
\n" ); document.write( "Write a time equation:
\n" ); document.write( "Time = \"distance%2Fspeed\"
\n" ); document.write( ":
\n" ); document.write( "Actual time = faster time + 1 hr
\n" ); document.write( "\"600%2Fx\" = \"600%2F%28%28x%2B20%29%29\" + 1
\n" ); document.write( ":
\n" ); document.write( "Multiply equation by x(x+20) to get rid of the denominators:
\n" ); document.write( "x(x+20)*\"600%2Fx\" = x(x+20)*\"600%2F%28%28x%2B20%29%29\" + x(x+20)(1)
\n" ); document.write( ":
\n" ); document.write( "Cancel out the denominators and you have;
\n" ); document.write( "600(x+20) = 600x + x(x+20)
\n" ); document.write( ":
\n" ); document.write( "600x + 12000 = 600x + x^2 + 20x
\n" ); document.write( ":
\n" ); document.write( "Arrange as a quadratic equation on the right
\n" ); document.write( "0 = x^2 + 20x + 600x - 600x - 12000
\n" ); document.write( ":
\n" ); document.write( "x^2 + 20x - 12000 = 0
\n" ); document.write( ":
\n" ); document.write( "Factors to:
\n" ); document.write( "(x+120)(x-100) = 0
\n" ); document.write( "Positive solution:
\n" ); document.write( "x = 100 mph actual speed
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check by finding the times of the two speeds
\n" ); document.write( "600/100 = 6 hr
\n" ); document.write( "600/120 = 5 hrs \n" ); document.write( "
\n" );