I have a map of Iowa on a Cartesian coordinate plane, where one unit represents approximately one minute of travel time. Des Moines is at the origin (0,0). Ames is at (0,30) . Iowa City is at (120,0) . Cedar Rapids is at (120,30) . How much farther is it from Iowa City to Ames than it is from Iowa City to Cedar Rapids? Express your answer in the form $a\pm b\sqrt{c}$ , where a and b are integers.