Math Is Fun Forum

bodie001

Member

Registered: 2010-01-05

Posts: 21

Wind Speed

a plane with a tailwind makes a 785-mile flight in 2.5 hours. The return flight against the wind takes half hour longer.  What is the wind speed?

I got 3 completely different answers:
52 Mph
288 mph
314 mph

Which one is correct?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Wind Speed

Hi bodie001;

Sorry, middle one is correct for the planes speed not the wind speed. Let's see what you did, so I can maybe help.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bodie001

Member

Registered: 2010-01-05

Posts: 21

Re: Wind Speed

I looked up average speeds of planes and then divided into 785 miles.  My first answer was 314mph.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Wind Speed

Yes, but the question is asking for the wind speed.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bodie001

Member

Registered: 2010-01-05

Posts: 21

Re: Wind Speed

Would it be something like

3x + y = 785?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Wind Speed

Hi;
This is an algebra question:
If we say p is the planes speed and w is the winds speed we get two equations:

p + w = 785 / 2.5
p  - w = 785 / 3

Add the 2 of them up to get:

2p = 575. 6666

Divide by 2 on both sides:

p = 287.8333 this is the planes speed. Now plug into the first equation:

287.8333 + w = 785 / 2.5 = 314

287.8333 + w = 314

w = 314 - 287.8333 = 26.1666 this is the winds speed

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Softtail Rider

Member

Registered: 2010-01-06

Posts: 3

Re: Wind Speed

Is this linear equations?  If so what is the inverse matrix method?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Wind Speed

Hi Softtail Rider;

Do not use a cannon to kill a mosquito.

That would solve that 2x2 linear set of simultaneous equations by inverting the matrix. This should be done by gaussian elimination. The problem of solving a nxn simul. is central in numerical analysis. There are dozens of ways to do it by why would you use any of them on such a simple problem?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Sarah Rebekah 13

Guest

Re: Wind Speed

Hey Bobbym did you see where I asked you What kind of home did you buy?

Softtail Rider

Member

Registered: 2010-01-06

Posts: 3

Re: Wind Speed

because I think I got a* b on a problem and was just curious what the inverse of b would on this one.

a = 4 -2
     1 3
     0 1

b= 5 2
    -1 3

I got answer of

22 2
2 11
-1 3

Just curious as to the answer.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Wind Speed

HI;

That is just matrix multiplication

The inverse of b is:

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Wind Speed

Hi;

Without getting too much jargon and without much rigor, to solve that problem using matrix inversion; we start with the matrix equation.

plugging into the matrix equation:

Now to get

by itself if this were a normal equation we would divide both sides by A. But in matrix algebra there is no division operator, instead we have the inverse of A. The inverse of A is:

Now when you multiply both sides by A^(-1) you get;

Which is what we got by more prosaic methods earlier.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.