Carmen drove from Blairtown to Ore City, a distance of 80 miles. From Ore City she drove to Janesville, and the drove back to Blairtown. The ratio of Carmen's driving times on the first, second, and third segments of the trip, respectively, was 5:2:4, and she drove at the same average speed on each segment. What was Carmen's total driving distance, in miles, for the 3 segments of the trip?

I know it is 176, but how do I show it algebraically?