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 December 14th, 2012, 05:55 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, 06:21 PM #2 Senior Member   Joined: Jul 2012 From: DFW Area Posts: 642 Thanks: 99 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, 06:33 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, 06:47 PM   #4
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Re: Word Problem

Quote:
 Originally Posted by tallbabe1 What is the rate of the plane in still air and what is the rate of the wind?
Does this mean that the answer would be a fraction because it says what is the rate? December 14th, 2012, 06:52 PM #5 Senior Member   Joined: Jul 2012 From: DFW Area Posts: 642 Thanks: 99 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, 06:59 PM   #6
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Re: Word Problem

Quote:
Originally Posted by tallbabe1
Quote:
 Originally Posted by tallbabe1 What is the rate of the plane in still air and what is the rate of the wind?
Does this mean that the answer would be a fraction because it says what is the rate?
Unfortunately I am leaving out units, which I should not really do. But I was trying to keep from cluttering up the equations. The units used are km and hr, so the speeds are in which is consistent with the equations. For example, when we divided by 4 in the first equation we were dividing: December 14th, 2012, 07:00 PM   #7
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Re: Word Problem

Quote:
Originally Posted by tallbabe1
Quote:
 Originally Posted by tallbabe1 What is the rate of the plane in still air and what is the rate of the wind?
Does this mean that the answer would be a fraction because it says what is the rate?
Rate is same as speed...don't try complicating things  December 14th, 2012, 07:13 PM #8 Member   Joined: Dec 2012 Posts: 30 Thanks: 0 Re: Word Problem So I did the first equation: 4(679-w)=2436 2716-4w=2436 -4w=-280 w=70 wind 70 Speed 679 So simplified is 10/97 Am I doing this right? December 14th, 2012, 07:20 PM #9 Senior Member   Joined: Jul 2012 From: DFW Area Posts: 642 Thanks: 99 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, 07:44 PM #10 Senior Member   Joined: Jul 2012 From: DFW Area Posts: 642 Thanks: 99 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 Tags problem, word Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post angelina Elementary Math 7 August 9th, 2010 11:18 PM hemi Algebra 3 September 15th, 2009 03:48 PM Hello Elementary Math 3 September 6th, 2008 04:47 AM iReap Algebra 2 February 10th, 2008 06:37 PM chak_2007 Elementary Math 5 September 13th, 2007 04:23 AM

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