# Rate word problem: speed of a plane in still air and distance traveled.

1. Jul 15, 2012

### Juxtaroberto

1. The problem statement, all variables and given/known data

So, I don't have the actual problem in front of me, but from my scribbles I can make out all the information the word problem gave. A plane flies from one place to another with the wind in 6 hours, and back against the wind, in 7 hours. The speed of the plane in still air is 13 times the speed of the wind. Find the speed of the plane in still air, the speed of the wind. Might have also asked for the distance traveled, not sure, though.

2. Relevant equations

d=rt

3. The attempt at a solution

I set something up like d=(x+c)(6) and d=(x-c)(7) and x=13c where d is the distance traveled, x is the speed of the plane, and c is the wind working against or for the plane. Because the first two equations are equal to d, I thought about setting them equal to each other, but all I get is either x=13c or c=(1/13)(x), which I was already told in the question. I'm assuming that this is a little different than other rate problems, because they gave me the time it took to arrive and come back, but not any of the speeds... I don't know. I've tried working on this problem in many different ways but I always end up at something like 84c=84c, which is true, of course, but which tells me nothing.

2. Jul 15, 2012

### eumyang

It feels like some information is missing from the problem. Please double check the place where you got the problem. In problems I've seen that were similar to this one, the distance was given.