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.
To find out how many meters away from the finish line Dan was when Fan crossed the finish line, we need to calculate the distance difference between the two runners.
We know that when Fan was at the 800 meter mark, Dan was 300 meters away from the finish line. This means that Dan had 300 meters left to run.
Since the total distance of the competition is 1000 meters, we can calculate the distance from the finish line for Dan when Fan crossed it by subtracting the distance Dan had left from the total distance.
So, we have:
Distance from the finish line for Dan = Total distance - Distance left for Dan
Distance from the finish line for Dan = 1000 meters - 300 meters
Distance from the finish line for Dan = 700 meters
Therefore, when Fan crossed the finish line, Dan was 700 meters away from the finish line.