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.)


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*(1/0.621371192)=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/(600+x)=2124/(600-x)}}}


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


{{{cross(600+x)(600-x)*2424/cross(600+x)=(600+x)cross(600-x)*2124/cross(600-x)}}}


{{{2424(600-x)=2124(600+x)}}}


*[invoke explain_simplification "2424(600-x)=2124(600+x)" ]


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