Ragtime rhymes with:
longtime, springtime, airtime, alltime, anytime, bedtime, centime, christmastime, daytime, dinnertime, downtime, everytime, flextime, fulltime, funtime, halftime, lifetime, longtime, lunchtime, maritime, mealtime, meantime, movietime, nighttime, noontime, overtime, parttime, pastime, peacetime, primetime, quicktime, schooltime, showtime, sometime, springtime, summertime, wartime, wintertime
Ragtime sounds like:
reaction, recitation, recoton, rectum, rejection, requisition, restaino, restitution, reston, resuscitation, ricadonna, richstone, richton, rigatoni, rigdon, risden, risdon, riston, rocketdyne, rosten, roston, roughton, royston, rushton, rustin, ruston