document.write( "Question 792516: A pilot flies a distance of 600 km. He could fly the same
\n" ); document.write( "distance in 30 minutes less time by increasing his average speed by
\n" ); document.write( "40 km/hr. Find his actual average speed.
\n" ); document.write( "

Algebra.Com's Answer #480035 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
A pilot flies a distance of 600 km. He could fly the same
\n" ); document.write( "distance in 30 minutes less time by increasing his average speed by
\n" ); document.write( "40 km/hr. Find his actual average speed.
\n" ); document.write( "-----------------
\n" ); document.write( "r = lower speed
\n" ); document.write( "r*t = 600 --> t = 600/r
\n" ); document.write( "(r+40)*(t-0.5) = 600
\n" ); document.write( "-----
\n" ); document.write( "Sub for t in the 2nd eqn
\n" ); document.write( "(r+40)*(600/r - 0.5) = 600
\n" ); document.write( "600 - 0.5r + 24000/r - 20 = 600
\n" ); document.write( "-0.5r + 24000/r = 20
\n" ); document.write( "-r + 48000/r = 40
\n" ); document.write( "r^2 - 48000 + 40r = 0
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B40x%2B-48000+=+0\") has the following solutons:
\n" ); document.write( "
\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
\n" ); document.write( "
\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%2840%29%5E2-4%2A1%2A-48000=193600\".
\n" ); document.write( "
\n" ); document.write( " Discriminant d=193600 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-40%2B-sqrt%28+193600+%29%29%2F2%5Ca\".
\n" ); document.write( "
\n" ); document.write( " \"x%5B1%5D+=+%28-%2840%29%2Bsqrt%28+193600+%29%29%2F2%5C1+=+200\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%2840%29-sqrt%28+193600+%29%29%2F2%5C1+=+-240\"
\n" ); document.write( "
\n" ); document.write( " Quadratic expression \"1x%5E2%2B40x%2B-48000\" can be factored:
\n" ); document.write( " \"1x%5E2%2B40x%2B-48000+=+%28x-200%29%2A%28x--240%29\"
\n" ); document.write( " Again, the answer is: 200, -240.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B40%2Ax%2B-48000+%29\"

\n" ); document.write( "\n" ); document.write( "==============
\n" ); document.write( "r = 200 km/hr
\n" ); document.write( "
\n" ); document.write( "
\n" );