Formula that predicts the location of moving enemy

Question

A rocket that explodes not on impact, but explodes on a timer will be shot from myself to the enemy. The timer can only be inputted at the start of the shot. The rocket can only go straight and has a speed of 1500m/s . The enemy is moving away from me in a straight line at a speed of 400m/s. The distance between myself and my enemy is 5000m. I need a formula that predicts the precise time until the rocket should explode so that it will explode directly on my enemy's location.

Answer 1

If they are going directly away from you, the problem is only one dimensional. Let us put you at $x=0$. Your enemy starts off at $x=5000$.

Your enemies position as a function of time is

$$ x_{enemy}=5000+400t $$

The rocket's position as a function of time is

$$ x_{rocket}=0+1500t $$

Set $x_{enemy}=x_{rocket}$ and solve for the $t$ at which they meet.

$$ 5000+400t=1500t\\ 5000+400t-400t=1500t-400t\\ 5000=1100t\\ \frac{5000}{1100}=\frac{1100t}{1100}\\ \frac{50}{11} = t\\ $$

It takes $\frac{50}{11}=4\frac{6}{11}$ seconds.