Car x leaves northtown traveling at a steady rate of 55 mph.  car y leaves 1 hour later following car x, traveling at a steady rate of 60 mph.  which equation can be used to determine how long after car x leaves car y will catch up?

Unfortunately, you haven't shared the equations from which you're supposed to choose your answer.

But we can write our own.

When will the distance traveled by the 1st car = the distance traveled by the 2nd car?

55 miles + (55 mph)x = (60 mph)x

solve this for x:  55 miles = (60-55)x mph = 5 mph

x=11 hours

The two cars are the same distance from the starting point after 11 hours.

The answer is option c.