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## I like Math, I always have

I helped my brother with his Math homework tonight. He's in Grade 9.

An aircraft travels 5432 km from Montreal to Paris in 7 h and returns in 8 h. The wind speed is constant. Determine the wind speed and the speed in still air.

```                                   ---> wind
Let x = speed in still air    M ---------------------> P
y = wind speed               v = (x + y)
d = 5432 km                  t = 7h```
```     d                             ---> wind
v = --- , d = vt              M <--------------------- P
t                           v = (x - y) km/h
t = 8h```
```Since the distance from A to B is the same as the distance from
B to A, we have:```
```    7x + 7y = 5432
8x - 8y = 5432```
`Add the two lines to get:`
```    15x - y = 10864
15x = 10864 + y```
`Subtract the two lines to get:`
```   -x + 15y = 0
x = 15y```
`Plug in '15y' for 'x':`
```       225y = 10864 + y
224y = 10864
y = 48.5```
`Plug in 'y':`
```          x = 15(48.5)
x = 727.5```
Wind speed: 48.5 km/h
Speed of aircraft in still air: 727.5 km/h

Q.E.D. Oct. 20th, 2001 01:14 pm (UTC)
Re: Hmmm.
Oh, and this was also bothering me the first time I read your solution, but I couldn't quite put my finger on it.

By calculating the velocity first and then half of the difference, you're introducing inaccuracy. In this case, the text book picked a nice number that was divisible by both 7 and 8. But in real life problems, you'd want to leave the exact number manipulation for the very end, if at all possible. You avoid rounding and preserve accuracy that way.

=) Oct. 20th, 2001 04:49 pm (UTC)
Re: Hmmm.
Except that the whole problem is silly in the first place, as the wind speed is never a constant anyways. It was a theoretical problem, just trivia.

In real life I'd never have to deal with it because I don't give a crap how fast the wind is blowing, and my job doesn't require that I know how fast it's blowing, or anything else similar. ;)

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