Rule #1 Name Stuff

Generally, Name what it is asking.

"How long after speeding up" There is your clue.(a) A highway patrolman traveling at the speed limit is passed by a car going 15 mph faster than he is. After one minute, the patrolman speeds up to 100 mph. How long after speeding up until the patrolman catches up with the speeding car. The speed limit is 55 mph.

t minutes = How long after speeding up.

Distance = Rate * Time

"After one minute"

Lead on Officer = 15 mph * 1 minute = Distance to Catch Up

There are some units problems there. Fix them before going on.

"the patrolman speeds up to 100 mph"

This one is a bit tricky. It appears we must assume this is instantaneous - a dubious assumption, indeed. In any case,

Distance to Catch Up = 25 mph * t minutes

You have some algebra before you...

There is no formal or official way to do this sort of thing. Organizing your brain is the important part. Lay it out untul it makes sense to you AND you can explain it to someone else.