Think as travelling north as travelling in the y-plane, and travelling west as in the x-plane.
(or more correctly)
After 2 hours, the first plane will have travelled 300km. (150x2)
We can model this as y = 300 + 150t, where t is the time in hours
After 2 hours, second plane will have just taken off and therefore travelled 0km.
We can model this as x = 200t, where t is the time in hours.
Now, think of this as a vector triangle question like in physics. This way we have a right-angled triangle, and we want the hypotenuse (the distance between the two planes) to be 600km.
Therefore we have:
Now we solve for :
Using a calculator to quickly solve the quadratic:
t = 1.48 hours or t = -2.92 hours
since t cannot be negative, t must be 1.48 hours (or 1.5 hours to the nearest tenth of an hour).
This is just a solution to the problem. There may (and hopefully should) be a much easier way to solve it, maybe given as an example somewhere in your book. If not, I hope this helps.