Christy and cindy are running together. cindy thinks christy runs a little slow, so she gives christy a 1.5 km advantage. this means cindy is at the starting point and christy is 1.5 km in front. cindy runs 0.22 km per minute and christy runs 0.12 km per minute. how long will it take before cindy catches up to christy?

Let´s:
t=time when the  both runners coincide.
velocity=distance/time  ⇒ distance=velocity x time 
distance traveled by Christy=0.12 t 
distance traveled by Cindy=0.22 t

Becuse  Christy starts the race with an advantage of 1.5 km de distance from Cindy´s position the distance would be : 0.12 t + 1.5
We would have to solve the following equation:
0.12t+1.5=.0.22t
0.22t-0.12t=1.5
0.1t=1.5
t=1.5/0.1
t=15

In 15 minutes Cindy will  catch Christy