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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?

 Sep 1, 2023
 #1
avatar+36926 
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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 

 Sep 1, 2023
 #2
avatar+36926 
0

....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 

ElectricPavlov  Sep 1, 2023

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