December 14th, 2012, 06:55 PM  #1 
Member Joined: Dec 2012 Posts: 30 Thanks: 0  Word Problem
An airplane travels 2436 km against the wind in 4 hours and 2996 km with the wind in the same amount of time( 4 hours). What is the rate of the plane in still air and what is the rate of the wind?

December 14th, 2012, 07:21 PM  #2 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 634 Thanks: 96 Math Focus: Electrical Engineering Applications  Re: Word Problem
We have two equations and two unknowns. If we assign w as the wind speed and a as the airplane's speed, then the first part of the problem statement yields the equation: Can you use the second part of the problem statement to come up with the second equation and solve? Please reply if you get stuck. 
December 14th, 2012, 07:33 PM  #3 
Member Joined: Dec 2012 Posts: 30 Thanks: 0  Re: Word Problem
Do I take both equations and set them equal to each other?

December 14th, 2012, 07:47 PM  #4  
Member Joined: Dec 2012 Posts: 30 Thanks: 0  Re: Word Problem Quote:
 
December 14th, 2012, 07:52 PM  #5 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 634 Thanks: 96 Math Focus: Electrical Engineering Applications  Re: Word Problem
In this case I would add the equations together to eliminate w as follows: divide by 4: (1) The other equation is: divide by 4: (2) Adding (1) plus (2) gives: so and Now you can solve either equation for w. 
December 14th, 2012, 07:59 PM  #6  
Senior Member Joined: Jul 2012 From: DFW Area Posts: 634 Thanks: 96 Math Focus: Electrical Engineering Applications  Re: Word Problem Quote:
 
December 14th, 2012, 08:00 PM  #7  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,943 Thanks: 985  Re: Word Problem Quote:
 
December 14th, 2012, 08:13 PM  #8 
Member Joined: Dec 2012 Posts: 30 Thanks: 0  Re: Word Problem
So I did the first equation: 4(679w)=2436 27164w=2436 4w=280 w=70 wind 70 Speed 679 So simplified is 10/97 Am I doing this right? 
December 14th, 2012, 08:20 PM  #9 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 634 Thanks: 96 Math Focus: Electrical Engineering Applications  Re: Word Problem
Well, you worked it correctly except at the end. The airplane, a and wind, w speeds are: and You should not have taken the ratio. Give me a little time and I will make a follow up post with the full solution including units. 
December 14th, 2012, 08:44 PM  #10 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 634 Thanks: 96 Math Focus: Electrical Engineering Applications  Re: Word Problem
Here is the full solution with units: Let a be the airplane's speed relative to the ground in km/hr. Let w be the wind speed relative to the ground in km/hr. So: and dividing by 4 hr gives: so (1) Notice that equation (1) is dimensionally consistent: a and w are both in km/hr (and so is their difference) on the left side and 609 is in km/hr on the right side. We also have: and dividing by 4 hr gives: so (2) Equation (2) is also dimensionally consistent: a and w are both in km/hr (and so is their sum) on the left side and 749 is in km/hr on the right side. Adding equation (1) to equation (2) we have: so Plugging this value into equation (2)  note that I am using this equation because it is slightly easier to present here: so 

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