X travels 40 miles in “2 hours and 40 minutes” = 160 minutes

Speed of X = 40/160 = 0.25mile/minute
= 15 miles/hr

X is 50 % faster than Y

Speed of y:

50 % of Speed of y = 15
= 30 miles/hr

Greg never solved the question this way in his three approaches. My doubt is if x is 50% faster than y , then how will y be expressed as a percentage of x

Hmm let a be the speed at which y travels so x travels 1.5 times of a(50% faster)
now since they are going in same direction the relative speed is 0.5a and the distance between them is 40miles so
40=0.5a*2.67(2.67=2hours 40 mins)

Percentage increase or decrease is not the right way to approach this problem. Relative speed as mentioned by Greg makes sense. One fact that people might find hard to wrap their head around is that they are travelling the same distance but we have to keep in mind that x covers 40 miles more. We use only that portion of the problem where x catches up with y to get the answer.

Let the speed of Y be y
and speed of X is y(1.50) (because it 50% faster than Y)
Let the distance covered by Y for 160 mins be x
and Distance covered by X for 160 mins be x+40

Therefore Considering Y
Speed= Distance/Time y=x/160
and x=160y

Considering X

y(1.50)=x+40/160
substitute x value

240y=160y+40 y=0.5 miles per minute
also y= 30 miles per hour