Special relativity, delay of a clock in a plane

[fluidistic]

Homework Statement

A plane is moving at 600m/s with respect to the ground. According to clocks on the ground, how much time would it take so that the plane's clock is delayed by 2 microseconds?

Homework Equations

Lorentz transformations.

The Attempt at a Solution

Let O be a reference frame on the ground and O' be a reference frame on the plane.
v=600m/s. If I'm not wrong, they ask me $$t_B-t_A$$ such that $$(t_B-t_A)-(t_A'-t_B')=2 \times 10 ^{-6}s$$. (*)
What I've done so far is $$t_B'-t_A'=\gamma \left [ t_B-t_A +\frac{v}{c^2}(x_A-x_B) \right ]$$, replacing $$x_A-x_B$$ by $$v(t_A-t_B)$$, then solving for $$t_B-t_A$$ in (*), I reach that it's worth exactly $$1000000s$$. Or 11 days, 13 hours, 46 minutes and 40 s. It seems too big for me. Do you get a different answer?

 

[collinsmark]

Your final answer is about the same as mine.

 

[fluidistic]

Your final answer is about the same as mine.

Oh ok. Thanks a lot for the confirmation.

 

[collinsmark]

Oh ok. Thanks a lot for the confirmation.

Be careful of your precision though. The speed of light isn't exactly 3.000000 x 10⁸ m/s. So I don't think you should be calculating the time down to the very second with that. But something around 1.0 x 10⁶ seconds is the answer that I got, is what I meant.