A. you are looking for the person who reached the distance (4 miles) the fastest. Since the black line has the most distance changed in the least amount of time, Ann wins the races and has the fastest rate of change. the green line stops growing next, so Kim has the second fastest rate of change and gets second. That means that the red line ends last, has the slowest rate of change, and Trey gets third. so the race goes 1. Ann 2. Kim 3. Trey
Rate of change (speed) just means the distance traveled divided by the time it took. so we can do this for each person. Ann traveled 4 miles in 12 minutes, so you do 4/12 and get her rate of change which is 1/3 or .33 repeating Next, we need to find Kim's rate of speed, so we take the distance she traveled (4 miles) divided by the time it took (16 minutes) if we do that we get 1/4 or .25 With Trey, he started at 2 miles, so his distance would be his final spot minus his starting spot, so he traveled 2 miles. if we take that and divide it by the time it took (18 minutes) we get 1/9 or .11 repeating.
Finally, we already found out that Ann has the fastest rate (1/3) and Trey has the slowest rate (1/9) we can prove this by stating that Ann traveled the most distance in the least amount of time. she traveled 4 miles in 12 minutes, which is greater than or equal to the other to distances by less than both times taken.
We can prove that Trey has the slowest rate because he traveled the least distance (2 miles) in the most time (18 minutes) that means that he took longer than the other two to travel less distance. his distance is less than the others and his time taken is greater than both of the other racers' times.
