Calculating Airplane Speed Using Time Dilation

[davesface]

An airplane travels at a constant speed v for a distance of 3000km as measured by a stationary observer. The pilot measures the flight time to be $\Delta t$ and the stationary observer measures the flight time to be $\Delta t'$. (Then I solved the first part of it, showing that $\Delta t' > \Delta t$.)

b. If $\left|\Delta t-\Delta t' \right|$=4ns, determine the speed of the airplane.

Now, I have tried every combination of plugging equations into one another that I could think of, and I always end up with some horrifically complicated equation in which it's impossible to solve for v. Suggestions on how to proceed from $\gamma\Delta t -\Delta t=4ns$

PS- The answer is 240m/s, but I cannot see at all how to get there.

 

[kuruman]

Can you state the whole problem as it is given, including part (a)? To check your work and help you out, we need to have all the information that you have.

 

[davesface]

a. Which time interval is longer? (As I said, I already showed that the t'>t)

 

[kuruman]

So you know Δt in terms of γ. Is there another way you can calculate Δt by first finding an expression for Δt' in terms of v and 3000 km?

 

[davesface]

Well, I can use $\Delta t=\frac{\Delta x}{v}$ to say that $\Delta t'=\gamma \frac{3,000,000}{v}$, but then that leads to an equation with a v² and a v term.

 

[davesface]

After 2 pages of fruitless attempts, I've decided to give up and hope for partial credit.