Dino, Kyle, and Nina race the 100 meters to the school bus each day. It develops that Dino and Kyle will reach the bus together if Dino is given a head start of 20 meters. Kyle and Nina will arrive together if Kyle is given a head start of 25 meters. If Dino and Nancy want to arrive at the bus at the same time, who should start where?
Solution
Let D, K, and N be Dino's, Kyle's, and Nancy's rates of speed.
Dino runs 80m when Kyle runs 100m, so D = (4/5)K.
Nina runs 100m when Kyle runs 75m, so K = (3/4)N.
So D = (4/5)(3/4)N = (3/5)N.
This means that when Nancy runs 100m, Dino runs 60m.
So give Dino a 40m head start.