Hugo and Brody each want to run for president of their school's student body council. In order to do so, they must collect a certain number of signatures and get a nomination. So far, Hugo has 27 signatures, and Brody has 23. Hugo is collecting signatures at an average rate of 10 per day, whereas Brody is averaging 14 signatures every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How long will that take? How many signatures will they both have?