What were the wind velocity and speed of the plane?

Question

A small plane flew 808 808 miles in 4 4 hours with the wind. Then on the return trip, flying against the wind, it traveled only 416 416 miles in 4 4 hours. What were the wind velocity and the speed of the plane? (Note: The "speed of the plane" means how fast the plane would be flying with no wind.)

Answer 1

Hi Sarah,

The easiest way to approach this problem is to set up two equations (one for traveling with the wind one for against).  Let the velocity of the plane be v.  Let the wind velocity be w.

So when the plane is traveling with the wind what is its velocity (relative to the earth)?   

The answer is :  v + w

Now that you have the velocity of the plane you can write the equation for its motion based on the relationship below:   Dist = rate x time 

This gives one equation.  Try to find the second equation.  If you can find both then the rest is algebra :^)>