You need to go where he is going to be, not where he was.
From your post, it looks to me like you're headed for where he was last reported. Obviously he's not gonna be there by the time you reach that location. He would've gone on a few miles.
You need to estimate where he will be in the time it takes for you to get there. It's called plotting an intercept course and speed.
Here's a simplified procedure:
a. Note which direction the contact is headed. Draw a line from the contact out along that direction. That is its base course.
b. Decide what speed the contact is going. Slow means about 7 kts; medium 10 and fast 12 kts (these are the rules of thumb I use).
c. Depending on the target's course and direction relative to you, decide how you want to intercept. A ship heading more or less towards you means you don't have a long distance to run. Conversely a contact headed away from you means you'll need to pour on the coal in order to overtake and get into position ahead of it.
d. Based on the above factors, make a mark on the target's course some time from now. Say two hours - so if the target is moving at 10 kts, he'll have covered 20 nm in 2 hours. That is the intercept point.
e. Next, decide whether it is feasible to reach that point based on your position and fuel available. If it's possible, plot a course for that point and ramp up the speed as necessary to reach that point before he does. Then wait for him to appear.
Do note that ships do change their base course. Take that into account. Many a time I've reached the intercept position only to find that the target has changed course and is now headed in a completely different direction.
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