If x is the place to finish, and t is the time,
t(x) = 125+5x for x=1,2,3
t(x) = 140+(168-140)/(10-3) x for x>3
= 140+4x
Create a piecewise function
t(x) = 125+5x for x=1,2,3
t(x) = 140+(168-140)/(10-3) x for x>3
= 140+4x
1. The winner comes in at a time of 130 minutes. This means the first-place finisher finishes at time 130.
So, for the first-place finisher: y = 130
2. The second-place finisher comes in at a time of 135 minutes. Since the time for each successive finisher increases by a regular interval, we can deduce that the second-place finisher's time is 135 and the interval is 5 minutes.
So, for the second-place finisher: y = 135
3. The third-place finisher comes in at a time of 140 minutes. Again, using the interval of 5 minutes, we can determine the third-place finisher's time and so on.
So, for the third-place finisher: y = 140
4. Continuing this pattern, we can determine the time for each successive finisher:
For the fourth-place finisher: y = 140 + 5
For the fifth-place finisher: y = 140 + 2 * 5
For the sixth-place finisher: y = 140 + 3 * 5
For the seventh-place finisher: y = 140 + 4 * 5
5. The last successful finisher gets 10th place with a time of 168 minutes. Therefore, we can determine the time for each successive finisher:
For the eighth-place finisher: y = 140 + 5 * (8 - 3)
For the ninth-place finisher: y = 140 + 5 * (9 - 3)
For the tenth-place finisher: y = 140 + 5 * (10 - 3)
Putting it all together, we have a piecewise function:
f(x) = {
130, x = 1
135, x = 2
140, x = 3
140 + (x - 3) * 5, 4 ≤ x ≤ 7
140 + 5 * (x - 3), 8 ≤ x ≤ 10
}
This function represents the placement (x) and corresponding time (y) for each contestant in the marathon race.