Question

Help me with this rate problem
An airplane travels 990 miles in 3 hours with the wind and makes the return trip in 3 hours and 40 minutes. Find the speed of the airplane in still air and the speed of the wind.

Answer 1

Okay, so for this problem, name two variables, say x and y that represent the speed of the airplane and wind respectively. With two variables, you need two equations. In the first situation, (x+y)3=990

Answer 2

nice problem

Answer 3

Two variables like, how many hours and minutes?

Answer 4

No the speeds of the wind and airplane

Answer 5

Oh yeah, because its asking to find the speed of airplane and wind

Answer 6

Yes, exactly. For the second equation, the wind and airplane are going opposite directions, so you subtract the speeds. (x-y)3(4/6)=990

Answer 7

So why did you put a 3 after the parenthesis?

Answer 8

The x+y is a speed so you multiply it by the time of the trip to find the distance of the trip.

Answer 9

So the number 3 is the number for 3 hours

Answer 10

yes

Answer 11

And in the second equation, 3(4/6) is 3 hours and 40 minutes in hours

Answer 12

then you just solve for x and y

Answer 13

Wait I don't understand where you gotten 4/6

Answer 14

I'm sorry if I am asking all these questions

Answer 15

No it's totally fine. I had to express 40 minutes in as hours so I divided it by 60 because there are 60 minutes in an hour

Answer 16

So 40/60 you made it simplified by 10 making it 4/6 correct?

Answer 17

Yes

Answer 18

Alright could you explain what to do next?

Answer 19

Now that I understand what number stands for what

Answer 20

Well you have to solve for x and y. To do that, turn the first equation into a y=(990-3x)/3

Answer 21

Then substitute that into the second equation to get (11/3)x+(11/3)((990-3x)/3)=990

Answer 22

11/3 is the same as 3(4/6) I just simplified it

Answer 23

\[\frac{ 11x }{ 3 }+\frac{ 10890-33x }{ 9 }=990\]

Answer 24

Where di you gt -33x

Answer 25

did you get

Answer 26

Okay wait I sec. I need to rethink this
Give me a moment

Answer 27

Because if you were to multiple 11/3 and 990-3x, shouldnt it be 10890/9x

Answer 28

wait 10890/-9x

Answer 29

its (990-3x)/3

Answer 30

but wait a moments

Answer 31

Okay I found an easier way to solve this. Let x equal the speed of the airplane when going with the wind. That means 3*x=990 and x=330

Answer 32

Let y equal speed of airplane when going against the wind. Thus we have (11/3)*y= 990 and y = 270

Answer 33

The difference between the two speeds is 60 and that is the difference between when the two speeds when the air is working with and working against, thus when the wind is not there, thus the difference between then the plane is working with the plane and flying in still air is half that distance or 30

Answer 34

So the speed of the plane in still air 300mph and the speed of the wind is 30mph

Answer 35

Could you reword that above of what you just said before your last response? I didn't quite get what you were saying

Answer 36

Just think about it as the average of the two speeds

Answer 37

Oh, So you are saying 330 with the wind and then you try to find out how fast the wind is going from the opposite direction which is 30, 330-30 = 300 mph

Answer 38

I still don't quite understand how you got 11/3 by simplifying 3(4/6)

Answer 39

4/6 =2/3

Answer 40

3(2/3)=(9+2)/3

Answer 41

Ohh okay, I see where you got it, you just had to make the fraction a mixed number to get 11/3, I keep forgetting my past year math skills

Answer 42

Cool. So do you understand everything now?

Answer 43

Alright one last question, where did you get 270? Did you divide 11/3 from 990?

Answer 44

Divide 990 by 11/3 which is the same as multiplying 990 by 3/11

Answer 45

Oh okay, Thank you very much, I understand what you were trying to explain to me

Answer 46

Awesome. I wish you all the best in all your future math endeavors. May the shwartz be with you.