Problem 13 (2023 AMC 8)

Along the route of a bicycle race, $7$ water stations are evenly spaced between the start and finish lines, as shown in the figure below. There are also $2$ repair stations evenly spaced between the start and finish lines. The 3rd water station is located $2$ miles after the 1st repair station. How long is the race in miles? [See figure in original PDF]