How Does Wind Affect the Flight Time of a Plane on a Square Route?

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Homework Statement

A plane flies a square route with each side 1500m in length (north, west, south then east) If a wind was blowing from the east at 20 km/h the entire trip, find the total time it will take for the plane to complete the journey, given that the plane is flying at 80 km/h

Homework Equations

t = d/v
vog = vom + vmg? (except this is in the air)

The Attempt at a Solution

since its a square, i figure the relative velocity of all directions will be the same.
i used pythagorean theorem to find the velocity of the plane when it is affected by the wind. i got 82.46 km/h. then i used the formula t = d/v.
i used 1500m x 4 (because there are 4 routes in the square). converted this to 6 km.
then divided it by the relative velocity (82.46 km/h)
this worked out to be around 262 seconds.
the answer is supposed to be 280 seconds.

what did i do wrong?

 

[hage567]

since its a square, i figure the relative velocity of all directions will be the same.

No, this is not a correct assumption. Think about what happens when the plane flies west (in the same direction as the wind). What will be the relative velocity in that case? What about when the plane is flying eastwards (into the wind)? How do the velocities add up then?

You must consider each side of the square separately.