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 $10$ km behind, and Foley is $15$ km behind. When Edith finishes the race, how far behind is Foley, in km?

Hi6942O Jun 16, 2024

#2**+1 **

Let's find how far everyone ran when Dirk finished.

When Dirk finishes, Edith has ran 14km while Foley has only ran 9km.

This means that Foley runs only 9/14 as fast as Edith.

We can now find how far Foley ran when Edith finished the race.

Plugging in 24, we find that Foley has only ran \(24 (9/14) ≈ 15.43 km\) when Edith ran 24.

This means Foley was \(24 - 15.43 ≈ 8.57\)km behind Edith.

So our final answer is 8.57km.

Thanks! :)

NotThatSmart Jun 16, 2024