Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $5$ km behind, and Foley is $6$ km behind. When Edith finishes the race, how far behind is Foley, in km?
+36919 x = time of D finish
E rate = 19/x time needed for E to finish = d/ rate = 5 km / ( 19/x) = 5x / 19
F rate = 18/x
Howo far does F run in 5x/19 ? d = r * time
d = 18/x * 5x /19 = 90/19 km
added to his 18 km = 22 14/19 km ....which is 1 5/19 km behind Edith as she finishes the 24 km
+36919 ....or as a simple ratio
Edith can run 19 in the time it takes Foley to run 18
18 is to 19 as x is to 24
18 / 19 = x / 24
x = 24 * 18/19 = 22 14/19 or 1 5/19 km behind Edith
