SOLUTION: 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

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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.)
Answer by drj(1380) About Me  (Show Source):
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.)

Step 1. distance=speed * time

Step 2. Let x be the speed of the wind.

Step 2. Let 600+x be the speed of the plane and the speed of the wind.

Step 3. Let t be the time it takes to go 1500 miles

Step 4. Then, (600 km/hour+x)t=1500 miles since distance traveled is 1500 miles.

Step 5. Convert 1500 miles into kilometers where 1 kilometer = 0.621371192 miles

1500%2A%281%2F0.621371192%29=2424

So in Step 4, it becomes (600+x)t=2424

Step 6. Let 600-x be the speed going in the other direction

Step 7. Then, (600-x)t=2424-300=2124 km since 300 km to go in the same amount of time.

Step 8. Solve for t in Steps 5 and 7 and set the equations equal to each other.

t=2424%2F%28600%2Bx%29=2124%2F%28600-x%29

Step 9. Multiply by (600+x)(600-x) to both sides of the equation to get rid of the denominators.



2424%28600-x%29=2124%28600%2Bx%29

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=39.5778364116095.
  • 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) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
This is an equation! Solutions: x=39.5778364116095.

Universal Simplifier and Solver


Done!



Step 10. Check times if equal: t=2424/(600+39.6)=3.79 hours, and t=2124/(600-39.6)=3.79 hours.

Step 11. ANSWER: So the wind speed is 39.6 km/hr.

I hope the above steps were helpful.

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.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV