The stations are sending out signals at the speed of light or 982
The difference in their signals is 860
Let the stations be at some points on the x-axis: (116,0) and (-116,0) and the ship be on the line y=80.
Since it took 860 microseconds longer for the signal to arrive from one station than the other, say station A and station B, the difference in their distances( ) to the ship at that time is (982)(860)=844520 ft.
Using the hyperbola equation:
In the derivation of the hyperbola equation, one can let . Do that here.
If we let the difference in our distances equal 2a, then
a=159.95/2=79.97 miles. So,
Since the distance from the origin to either focus is 116,
Therefore, an equation for the hyperbola is:
Setting y=80 and solving for x, we find x=110.43
So, the coordinates of the ship are approximately (110.43,80).
I hope I didn't go off on a tangent somewhere. Get it?.Tangent?. Get it?.