# Systems of Equations: Word Problem

1. Feb 21, 2012

### S.R

1. The problem statement, all variables and given/known data
A small plane flying into the wind takes 3 h 20 min to complete a flight of 960km. Flying with the wind, the same plane takes 2 h 30 mins to make the trip. What is the speed of the plane? What is the speed of the wind?

2. Relevant equations
N/A

3. The attempt at a solution
I'm unsure on how to set-up the two equations:

Let x represent the speed of the plane and y represent the speed of the wind.

7/3(x-y)=960

5/2(x+y)=960

Is this representation correct?

2. Feb 21, 2012

### Staff: Mentor

Looks good to me. Now solve for x and y.

3. Feb 21, 2012

### S.R

EDIT: The mistake is 7/3; it is suppose to be 10/3.

Rewriting:

10x-10y=2880

5x+5y=1920

or

5x-5y=1440

5x+5y=1920

10x=3360

x=336

Substituting:

5(336)+5y=1920

1680+5y=1920

y=48

Last edited: Feb 21, 2012
4. Feb 21, 2012

### Staff: Mentor

Sorry, I didn't notice before, but 3hr 20 min = 10/3 hr, not 7/3 hr.

5. Feb 21, 2012

Thanks .