Equation involving 2 variables

[r0bHadz]

Homework Statement

A plane travels 3000 mi in 4 hours, when the wind is favorable the plane averages 900 mph. When the wind is unfavorable the wind averages 500 mph. During how many hours was the wind favorable.

Homework Equations

The Attempt at a Solution

To me this looks like a simple equation. Let x stand for favorable wind

900x + 500y = 3000

y = (1/500)(3000-900x)

the book is telling me the answer is 5/2 hours.

plugging 5/2 gives me a y value that satisfies the equation, but I am wondering, wouldn't the equation be satisfied for all values of y, s.t. 0<x≤3

meaning the plane could have flew for 2 hours in favorable win, and 2.4 hours in unfavorable wind, and my answer would still be correct?

 

[pasmith]

You have forgotten the constraint that $x + y = 4$.

 

[r0bHadz]

You have forgotten the constraint that $x + y = 4$.

That makes sense lol. TY

 

[Mark44]

To me this looks like a simple equation. Let x stand for favorable wind

This is not useful.
x needs to be a number. What attribute of "favorable wind" can be represented by a number?

A better description would be "Let x = the number of hours of the flight in which there was favorable wind."

900x + 500y = 3000

And here, y would probably represent the number of hours of the flight with an unfavorable wind.

When you assign meanings to variables, take care to come up with meaningful meanings.

You have forgotten the constraint that $x + y = 4$.

That makes sense lol. TY

It would have been easier to make the connection that @pasmith showed if you had identified your variables in a clearer way.