My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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?
tallbabe1 is offline  
 
December 14th, 2012, 06:21 PM   #2
jks
Senior Member
 
jks's Avatar
 
Joined: Jul 2012
From: DFW Area

Posts: 635
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.
jks is offline  
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?
tallbabe1 is offline  
December 14th, 2012, 06:47 PM   #4
Member
 
Joined: Dec 2012

Posts: 30
Thanks: 0

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?
tallbabe1 is offline  
December 14th, 2012, 06:52 PM   #5
jks
Senior Member
 
jks's Avatar
 
Joined: Jul 2012
From: DFW Area

Posts: 635
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.
jks is offline  
December 14th, 2012, 06:59 PM   #6
jks
Senior Member
 
jks's Avatar
 
Joined: Jul 2012
From: DFW Area

Posts: 635
Thanks: 96

Math Focus: Electrical Engineering Applications
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:

jks is offline  
December 14th, 2012, 07:00 PM   #7
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,321
Thanks: 1023

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
Denis is online now  
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?
tallbabe1 is offline  
December 14th, 2012, 07:20 PM   #9
jks
Senior Member
 
jks's Avatar
 
Joined: Jul 2012
From: DFW Area

Posts: 635
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.
jks is offline  
December 14th, 2012, 07:44 PM   #10
jks
Senior Member
 
jks's Avatar
 
Joined: Jul 2012
From: DFW Area

Posts: 635
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



jks is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
problem, word



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
ANOTHER... word problem! angelina Elementary Math 7 August 9th, 2010 11:18 PM
Word problem hemi Algebra 3 September 15th, 2009 03:48 PM
Word Problem Hello Elementary Math 3 September 6th, 2008 04:47 AM
Word Problem iReap Algebra 2 February 10th, 2008 06:37 PM
word problem chak_2007 Elementary Math 5 September 13th, 2007 04:23 AM





Copyright © 2019 My Math Forum. All rights reserved.