document.write( "Question 230598: An executive flew in the corporate jet to a meeting in a city 1500 miles away. After traveling the same amount of time on the return flight, the pilot mentioned that they still had 300 kilometers to go. The speed of the plane was 600 kilometers per hour. How fast was the wind blowing? (Assume that the wind direction was parallel to the flight path and constant all day.) \n" ); document.write( "
Algebra.Com's Answer #170796 by drj(1380)\"\" \"About 
You can put this solution on YOUR website!
An executive flew in the corporate jet to a meeting in a city 1500 miles away. After traveling the same amount of time on the return flight, the pilot mentioned that they still had 300 kilometers to go. The speed of the plane was 600 kilometers per hour. How fast was the wind blowing? (Assume that the wind direction was parallel to the flight path and constant all day.)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 1. distance=speed * time\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 2. Let x be the speed of the wind.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 2. Let 600+x be the speed of the plane and the speed of the wind.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 3. Let t be the time it takes to go 1500 miles\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 4. Then, (600 km/hour+x)t=1500 miles since distance traveled is 1500 miles. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 5. Convert 1500 miles into kilometers where 1 kilometer = 0.621371192 miles\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"1500%2A%281%2F0.621371192%29=2424\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So in Step 4, it becomes (600+x)t=2424\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 6. Let 600-x be the speed going in the other direction\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 7. Then, (600-x)t=2424-300=2124 km since 300 km to go in the same amount of time.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 8. Solve for t in Steps 5 and 7 and set the equations equal to each other.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"t=2424%2F%28600%2Bx%29=2124%2F%28600-x%29\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 9. Multiply by (600+x)(600-x) to both sides of the equation to get rid of the denominators.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2424%28600-x%29=2124%28600%2Bx%29\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

\n" ); document.write( "
\n" ); document.write( "

\n" ); document.write( " YOUR ANSWER\n" ); document.write( "


\n" ); document.write( "\n" ); document.write( "
    \n" ); document.write( "
  • This is an equation! Solutions: x=39.5778364116095.
    • \n" ); document.write( "
  • Graphical form: Equation \"2424%2A%28600-x%29=2124%2A%28600%2Bx%29\" was fully solved.
  • Text form: 2424*(600-x)=2124*(600+x) simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+2424%2A%28600-x%29=2124%2A%28600%2Bx%29+%29\"
    For tutors: simplify_cartoon( 2424*(600-x)=2124*(600+x) )
    • \n" ); document.write( "
  • If you have a website, here's a link to this solution.
    • \n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "

DETAILED EXPLANATION

\n" ); document.write( "
Look at \"2424%2A%28highlight_red%28+600+%29-x%29=2124%2A%28600%2Bx%29\".
Moved \"600\" to the right of expression
It becomes \"2424%2A%28-x%2Bhighlight_green%28+600+%29%29=2124%2A%28600%2Bx%29\".
\n" ); document.write( "
Look at \"2424%2A%28-x%2B600%29=2124%2A%28highlight_red%28+600+%29%2Bx%29\".
Moved \"600\" to the right of expression
It becomes \"2424%2A%28-x%2B600%29=2124%2A%28x%2Bhighlight_green%28+600+%29%29\".
\n" ); document.write( "
Look at \"2424%2A%28-x%2B600%29=highlight_red%28+2124%2A%28x%2B600%29+%29\".
Moved these terms to the left \"highlight_green%28+-2124%2A%28x%2B600%29+%29\"
It becomes \"2424%2A%28-x%2B600%29-highlight_green%28+2124%2A%28x%2B600%29+%29=0\".
\n" ); document.write( "
Look at \"highlight_red%28+2424%2A%28-x%2B600%29+%29-2124%2A%28x%2B600%29=0\".
Expanded term \"2424\" by using associative property on \"%28-x%2B600%29\"
It becomes \"-highlight_green%28+2424%2Ax+%29%2Bhighlight_green%28+2424%2A600+%29-2124%2A%28x%2B600%29=0\".
\n" ); document.write( "
Look at \"-2424%2Ax%2Bhighlight_red%28+2424+%29%2Ahighlight_red%28+600+%29-2124%2A%28x%2B600%29=0\".
Multiplied numerator integers
It becomes \"-2424%2Ax%2Bhighlight_green%28+1454400+%29-2124%2A%28x%2B600%29=0\".
\n" ); document.write( "
Look at \"-2424%2Ax%2Bhighlight_red%28+1454400+%29-2124%2A%28x%2B600%29=0\".
Moved \"1454400\" to the right of expression
It becomes \"-2424%2Ax-2124%2A%28x%2B600%29%2Bhighlight_green%28+1454400+%29=0\".
\n" ); document.write( "
Look at \"-2424%2Ax-highlight_red%28+2124%2A%28x%2B600%29+%29%2B1454400=0\".
Expanded term \"-2124\" by using associative property on \"%28x%2B600%29\"
It becomes \"-2424%2Ax-highlight_green%28+2124%2Ax+%29-highlight_green%28+2124%2A600+%29%2B1454400=0\".
\n" ); document.write( "
Look at \"-2424%2Ax-2124%2Ax-highlight_red%28+2124+%29%2Ahighlight_red%28+600+%29%2B1454400=0\".
Multiplied numerator integers
It becomes \"-2424%2Ax-2124%2Ax-highlight_green%28+1274400+%29%2B1454400=0\".
\n" ); document.write( "
Look at \"-2424%2Ax-2124%2Ax-highlight_red%28+1274400+%29%2Bhighlight_red%28+1454400+%29=0\".
Added fractions or integers together
It becomes \"-2424%2Ax-2124%2Ax%2Bhighlight_green%28+180000+%29=0\".
\n" ); document.write( "
Look at \"-highlight_red%28+2424%2Ax+%29-highlight_red%28+2124%2Ax+%29%2B180000=0\".
Eliminated similar terms \"highlight_red%28+-2424%2Ax+%29\",\"highlight_red%28+-2124%2Ax+%29\" replacing them with \"highlight_green%28+%28-2424-2124%29%2Ax+%29\"
It becomes \"highlight_green%28+%28-2424-2124%29%2Ax+%29%2B180000=0\".
\n" ); document.write( "
Look at \"%28-highlight_red%28+2424+%29-highlight_red%28+2124+%29%29%2Ax%2B180000=0\".
Added fractions or integers together
It becomes \"%28highlight_green%28+-4548+%29%29%2Ax%2B180000=0\".
\n" ); document.write( "
Look at \"%28highlight_red%28+-4548+%29%29%2Ax%2B180000=0\".
Removed extra sign in front of \"-4548\"
It becomes \"%28-highlight_green%28+4548+%29%29%2Ax%2B180000=0\".
\n" ); document.write( "
Look at \"highlight_red%28+%28-highlight_red%28+4548+%29%29%2Ax+%29%2B180000=0\".
Remove unneeded parentheses around factor \"highlight_red%28+4548+%29\"
It becomes \"-highlight_green%28+4548+%29%2Ax%2B180000=0\".
\n" ); document.write( "
Look at \"highlight_red%28+-4548%2Ax%2B180000+%29=0\".
Solved linear equation \"highlight_red%28+-4548%2Ax%2B180000=0+%29\" equivalent to -4548*x+180000 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: x=39.5778364116095.

Universal Simplifier and Solver

\n" ); document.write( "
Done!

\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 10. Check times if equal: t=2424/(600+39.6)=3.79 hours, and t=2124/(600-39.6)=3.79 hours.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Step 11. ANSWER: So the wind speed is 39.6 km/hr.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I hope the above steps were helpful.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "And good luck in your studies!\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J\r
\n" ); document.write( "\n" ); document.write( "http://www.FreedomUniversity.TV \n" ); document.write( "
\n" );