Around the same period of time, both Maids of Might seemingly showed up the Fastest Men Alive, and tension was definitely thick in the air. Blame the crotchety demeanor on each Flash's part due to their Midwestern sensibilities, and not wanting the be showed up by the fairer sex.
Barry-Flash had met Supergirl on a few occasions, sometimes in the company of her older cousin Supergirl and even when she teamed up the Justice League to save him from mental mastermind Despero. However, at this point Barry-Flash and fellow Leaguer the Atom were on the trail of a crimelord, and ended up getting drawn into a trap set forth by their old foe the wand-wielding T.O. Morrow on an alien world. Supergirl first seemed the irritating interloper yet later showed her worth helping protect the Leaguer's ladies Iris Allen and Jean Loring.
Meanwhile, Power Girl had just helped the Justice Society combat mental mastermind Brain Wave after having just debuted as a superheroine, and tried to earn the respect of her new teammate Jay-Flash by challenging him to a race, one that he won. However, she proved her worth to him and the other Socialites by playing a part in the defeat of the axe-wielding Vulcan.
An interesting aside, first Supergirl and then Barry-Flash would be forever connected when both perished defending the Multiverse during the Crisis on Infinite Earths. Something their counterparts Power Girl and Jay-Flash forevermore appreciated.