You leave your house for school at 8 AM, driving the 
speed limit of 30 mph.  A half hour later, WHEN YOU 
ARE 15 MILES FROM HOME SINCE DISTANCE=RATE×TIME = 
30(1/2)=15, your mother realizes that you 
forgot your socks.  She jumps in her car and speeds 
towards you at 80 mph.  SO HER CATCH-UP RATE IS 80-30 
OR 50 MPH.  At what time will your mother catch up to 
you?  SINCE TIME=DISTANCE/RATE, SHE'LL CATCH-UP YOUR 
15 MILES HEAD START IN 15/50 or 3/10 OF AN HOUR (OR 
18 MINUTES AT 8:18AM). How far are the two of you from 
home at this point? SINCE DISTANCE = RATE×TIME YOU'VE 
TRAVELED 30×(3/10) OR 9 MILES. 

Edwin