Dori and Malory are tracking their steps taken as a health goal. Dori leaves her house at 12:00 p.m. and walks at 50 steps per minute. Malory leaves her house at 12:20 p.m. and walks at 90 steps per minute.
At what time will Malory's steps catch up to Dori's steps?
Dori walks for 20 minutes before Malory leaves her house, which is a total of 20 minutes x 50 steps per minute = <<20*50=1000>>1000 steps.
Since Malory walks at a faster pace, it will take her 1000 steps / (90 steps/minute) = <<1000/(90/1)=11.11>>11.11 minutes to catch up to Dori.
Since Malory left her house at 12:20 p.m., she will catch up to Dori at 12:20 p.m. + 11 minutes = <<12.20+11=12.31>>12:31 p.m. Answer: \boxed{12:31}.