Word Problem Help? "Dave and Sandy are frequent flyers with a particular airline...."

[musiclady420]

Word Problem Help? "Dave and Sandy are frequent flyers with a particular airline...."

For whatever reason I always have issues with plugging in numbers to word problems. No matter what equation I memorize, I can never figure out where to plug in the numbers?!?!? For example, I know the equation
Rate x Time=Distance. Not that hard to figure out. Yet, when a "word problem" occurs, I am lost as to where to plug in these numbers! Once I see how to fill in the numbers I have no problems figuring out the linear equation in 2 or 3 variables. So, this simple question tonight just stumped me on how to begin? Like, how do I know what equation I should figure into the graph? So, here is my question. I do NOT need help with the linear equation part of it. Where I need the help is figuring out how to plug in the numbers to make the equations correct in the first place.

Question: Dave and Sandy are frequent flyers with a particular airline. They often fly from City A to City B, a distance of 876 miles. On one particular trip, they fly into the wind, and the flight takes 2 hours. The return trip, with the wind behind them; only takes 1 1/2 hours. If the wind speed is the same on each trip, find the speed of the wind and find the speed of the plane in still air.

What I know: I know they are asking for A) Wind speed and is it Hours, MPH, or Miles and B) The Speed of the Plane and is it Hours, MPH, or Miles.
I know both answers will be MPH.
I know that R x T=D.
I Realize that 876 needs to go in the D column of the chart.
I realize that my two times are 2 and 1 1/2, and need to be under the "Time" column.
I read the problem 5 times before I set up my chart.
I have no problem with "UNDERSTAND" the problem, "SOLVE" the problem, or "INTERPRET" the results.
My issue seems to happen during the step "TRANSLATE" the problem into 2 equations.

Where my confusion is happening: So I know my 2 "R" or rates will be x-y and x+y. Yet, I do NOT know why or which column to put them into or why? Because tonight, I got them backwards. So, I put (x+y) X 2=876 and the second column I put (x-y) X 1 1/2 =876. When the equations should be (x-y) X 2=876 and (x+y) X 1 1/2=876. The first equation is the speed of the plane and the second equation is wind speed. The only reason I knew it was wrong the first way I set it up is because I knew that the wind speed could NOT be 511 mph therefore the plane could NOT be traveling at 73MPH!

Also, for whatever reason this seems to be my "Achilles Heel" for word problems because it happens in pretty much every word I problem I do. So, I tried to remedy it by doing opposite of my original thoughts as to solve my "word problem" dilemma. Yet, there are plenty of time where my first assumption is correct therefore I still end up with wrong answers. I just hope someone else has experienced this and figured a way around it. I'm quite frustrated at this point. The only reason why I am continuing on is because I need the math courses for my degree.

 

[Dr.Peterson]

For whatever reason I always have issues with plugging in numbers to word problems. No matter what equation I memorize, I can never figure out where to plug in the numbers?!?!? For example, I know the equation
Rate x Time=Distance. Not that hard to figure out. Yet, when a "word problem" occurs, I am lost as to where to plug in these numbers! Once I see how to fill in the numbers I have no problems figuring out the linear equation in 2 or 3 variables. So, this simple question tonight just stumped me on how to begin? Like, how do I know what equation I should figure into the graph? So, here is my question. I do NOT need help with the linear equation part of it. Where I need the help is figuring out how to plug in the numbers to make the equations correct in the first place.

Question: Dave and Sandy are frequent flyers with a particular airline. They often fly from City A to City B, a distance of 876 miles. On one particular trip, they fly into the wind, and the flight takes 2 hours. The return trip, with the wind behind them; only takes 1 1/2 hours. If the wind speed is the same on each trip, find the speed of the wind and find the speed of the plane in still air.

What I know: I know they are asking for A) Wind speed and is it Hours, MPH, or Miles and B) The Speed of the Plane and is it Hours, MPH, or Miles.
I know both answers will be MPH.
I know that R x T=D.
I Realize that 876 needs to go in the D column of the chart.
I realize that my two times are 2 and 1 1/2, and need to be under the "Time" column.
I read the problem 5 times before I set up my chart.
I have no problem with "UNDERSTAND" the problem, "SOLVE" the problem, or "INTERPRET" the results.
My issue seems to happen during the step "TRANSLATE" the problem into 2 equations.

Where my confusion is happening: So I know my 2 "R" or rates will be x-y and x+y. Yet, I do NOT know why or which column to put them into or why? Because tonight, I got them backwards. So, I put (x+y) X 2=876 and the second column I put (x-y) X 1 1/2 =876. When the equations should be (x-y) X 2=876 and (x+y) X 1 1/2=876. The first equation is the speed of the plane and the second equation is wind speed. The only reason I knew it was wrong the first way I set it up is because I knew that the wind speed could NOT be 511 mph therefore the plane could NOT be traveling at 73MPH!

Also, for whatever reason this seems to be my "Achilles Heel" for word problems because it happens in pretty much every word I problem I do. So, I tried to remedy it by doing opposite of my original thoughts as to solve my "word problem" dilemma. Yet, there are plenty of time where my first assumption is correct therefore I still end up with wrong answers. I just hope someone else has experienced this and figured a way around it. I'm quite frustrated at this point. The only reason why I am continuing on is because I need the math courses for my degree.

Your problem is very common, and there is a simple solution.

The key here is knowing which of x-y and x+y represents which speed; and to get that right, it helps a lot if, rather than just "memorizing" them, you think about "why".

Another key is to clearly define your variables. Does x represent the plane's speed, or the wind's speed? It makes a big difference.

You have two times, 2 and 1.5 hours; you should label the rows in which you put them "into wind" and "with wind", respectively. When you say, "The first equation is the speed of the plane and the second equation is wind speed," that's wrong. One equation describes the flight into the wind (against the wind), and the other describes the flight with the wind. It is the variables, not the equations, that represent the plane's and the wind's speed. So labeling things carefully is really important.

Flying into the wind, you fly slower, right? That's because the wind is holding you back. So if x is the plane's speed, and y is the wind's speed, then the net speed is x - y: the wind speed subtracts from the plane's speed.

Flying with the wind, the wind adds to the plane's speed, making x + y.

Once that is clear, you can write the two equations:

Against wind: 2(x - y) = 876
With wind: 1.5(x + y) = 876

Solve those, and you get values for the plane's speed, x, and the wind's speed, y.

Summarizing, the main issue, I think, is that you are not thinking of the "translate" step as what it is: translation! To translate between two languages, you first have to know what the original statement means, and then to look up the appropriate words in the new language. You need a dictionary. So I suggest writing a dictionary:

x = plane's speed
y = wind speed
x + y = speed going with wind
x - y = speed going against wind

Once that is all written out (and, yes, you need to write it, not just think it!), the translation is easy. Translating without a dictionary is usually a disaster.

 

[Steven G]

For whatever reason I always have issues with plugging in numbers to word problems. No matter what equation I memorize, I can never figure out where to plug in the numbers?!?!? For example, I know the equation
Rate x Time=Distance. Not that hard to figure out. Yet, when a "word problem" occurs, I am lost as to where to plug in these numbers! Once I see how to fill in the numbers I have no problems figuring out the linear equation in 2 or 3 variables. So, this simple question tonight just stumped me on how to begin? Like, how do I know what equation I should figure into the graph? So, here is my question. I do NOT need help with the linear equation part of it. Where I need the help is figuring out how to plug in the numbers to make the equations correct in the first place.

Question: Dave and Sandy are frequent flyers with a particular airline. They often fly from City A to City B, a distance of 876 miles. On one particular trip, they fly into the wind, and the flight takes 2 hours. The return trip, with the wind behind them; only takes 1 1/2 hours. If the wind speed is the same on each trip, find the speed of the wind and find the speed of the plane in still air.

What I know: I know they are asking for A) Wind speed and is it Hours, MPH, or Miles and B) The Speed of the Plane and is it Hours, MPH, or Miles.
I know both answers will be MPH.
I know that R x T=D.
I Realize that 876 needs to go in the D column of the chart.
I realize that my two times are 2 and 1 1/2, and need to be under the "Time" column.
I read the problem 5 times before I set up my chart.
I have no problem with "UNDERSTAND" the problem, "SOLVE" the problem, or "INTERPRET" the results.
My issue seems to happen during the step "TRANSLATE" the problem into 2 equations.

Where my confusion is happening: So I know my 2 "R" or rates will be x-y and x+y. Yet, I do NOT know why or which column to put them into or why? Because tonight, I got them backwards. So, I put (x+y) X 2=876 and the second column I put (x-y) X 1 1/2 =876. When the equations should be (x-y) X 2=876 and (x+y) X 1 1/2=876. The first equation is the speed of the plane and the second equation is wind speed. The only reason I knew it was wrong the first way I set it up is because I knew that the wind speed could NOT be 511 mph therefore the plane could NOT be traveling at 73MPH!

Also, for whatever reason this seems to be my "Achilles Heel" for word problems because it happens in pretty much every word I problem I do. So, I tried to remedy it by doing opposite of my original thoughts as to solve my "word problem" dilemma. Yet, there are plenty of time where my first assumption is correct therefore I still end up with wrong answers. I just hope someone else has experienced this and figured a way around it. I'm quite frustrated at this point. The only reason why I am continuing on is because I need the math courses for my degree.

Imagine that the plane can stay in the air with the plane NOT moving on its own. But the plane IS moving! Why, because the wind is moving it.

Say the wind is moving 50mph and the the plane is traveling on its own at 500mph. If the plane is going in the direction that the wind is blowing, then this helps the plane. So if you are on the ground you will see the plane moving at the rate of 500+50 =550mph.

Now what if the wind is blowing opposite that the plane is going. Say that the wind is blowing 50mph and the plane is traveling on its own at 50mph in the opposite direction, then you on the ground will see the plane not moving. The wind works against the plane. Again, if the wind is 50mph and the plane is going in the opposite direction at 500mph, then you on the ground will see the plane going 500-50 = 450mph.