Math
posted by James .
Fan and Dan took part in a 1000 meter competition. When Fan was at the 800 meter mark, Dan was 300 meters away from the finish line. How many meters away from the finish line was Dan when Fan crossed the finish line?

100 m

let the time at which was at the 800 m mark be t
then Fran's rate = 800/t
Dan's rate = 300/t
Let the time it took Fran to run the whole 1000 m be k
1000 = k(800/t)
k = 1000t/800
in that same time of k, distance covered by Dan was
D = k(300/t) , using Distance = rate x time
= (1000t/800)(300/t) = 375
so Dan is still 625 m from the finish line when Fran crosses. 
I think I misread the question.
Dan was 300 m from the finish line, so he had gone 700 m, I took it that he went 300 m
so change all my 300's to 700
D = (1000t/800)(700/t) = 875
so he was 125 m from the finish line.
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