Alright, lets get started.
Roger can run one mile in 18 minutes.
Jeff can run one mile in 15 minutes.
Suppose in x minutes, they both will catch up.
Roger runs in 18 minutes = 1 mile
So, Roger will run in 1 minute = miles
So, Roger will run in x minutes = miles
Jeff runs in 15 minues = 1 mile
So, Jeff will run in 1 minute = mile
As Jeff gives roger a 1 minute head start, means Jeff will have x-1 minute time to run
So, Jeff will run in (x-1) minute =
As both are cathing up means they both runs same distance, means
Cross Multiplying
x = 6 minutes
So for calculating distance =
Distance = miles
It means it will take 1/3 or 0.33 miles before jeff catches up to roger. : Answer
Hope it will help :)