"In time" versus "on time"

Solution 1:

"In time" usually has an implicit "for (some event)", whereas "on time" means "before some deadline".

The "event" could be a deadline, but in that case "on time" is much more common.

Examples:

"I got there in time for the parade"

"I delivered the report in time for him to read it before the meeting"

"I got to town in time (for)/(to catch) the last train"

"I got there in time" - meaning "in time for some event which is assumed to be known".

but

"I got there on time" - meaning "before the deadline" - which may be known to the hearer, but does not need to be, because the phrase itself implies a deadline as opposed to some other event.

Solution 2:

On time means at a particular designated time, i.e. neither especially early nor late. The train is scheduled to arrive on time at 13:36.

In time means early enough, i.e. before a deadline or another cutoff. Passengers were required to be at the gate by 3:05pm; we didn't get to the airport till 3, but there was no line at security, so we still made it in time.

Solution 3:

In this case, "on time" is the proper choice.

More details about the differences:

"In time" is used to suggest that I was able to perform an action before another event occurred:

I was able to reach you in time.

The difference between "in time" and "on time" would be deadlines or schedules that revolve around very specific date or hour:

The train was on time.

The project was completed on time.

Of note, the phrases can also be used in other unrelated contexts:

(in music) Step in time.

Dorian Gray was stuck in time.