A Transmutation to the Past

It is the year 2014 and Rachel Hayashi is the Infinity Alchemist and the last state alchemist in the country of Amestris. When she and her younger sister, Emily, perform Human Transmutation to bring their youngest sister back, things don't go as planned. They go into a portal and somehow get transported back to 1914, exactly 100 years into the past. They are in they're home country of Amestis still and have no idea why the portal brought them here and how to get back. When they meet Edward and Alphonse Elric, they have some hope that they might be able to get back to their present time. With some conflicts with the Homunculi and other enemies, and very little time on their hands, the four of them have to work together to get Rachel and Emily home. (Don't worry this is full of comedy as well as seriousness :D)