NSEP Prep-2019

This is easy enough to do by searching the parameter space $(10 \leq x_1 \leq 12)$ and $(55 \leq x_2 \leq 60)$ , and by applying the "fourth second" qualifying condition.

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import math

N = 2000

#####################################

tfmax = 0.0
tfmin = 9999999999.0

dx1 = (12.0 - 10.0)/N   # Increments for x1,x2
dx2 = (60.0 - 55.0)/N

#####################################

x1 = 10.0

while x1 <= 12.0:   # search x1 between 10 and 12

    x2 = 55.0

    while x2 <= 60.0: # search x2 between 55 and 60

        v = (x2 - x1)/12.0  # speed from t = 12 condition

        #22.0 = x1 + v*tm 

        tm = (22.0 - x1)/v  # calculate time to pass x = 22

        if (tm >= 3.0) and (tm <= 4.0): # tm must be between 3 and 4
            qual = 1                    # this is the qualifying condition
        else:
            qual = 0

        tf = (88.0 - x1)/v      # calculate time to reach 88 meters

        if (tf > tfmax) and (qual == 1):  # store tfmin/tfmax, supervised by qual
            tfmax = tf

        if (tf < tfmin) and (qual == 1):
            tfmin = tf

        x2 = x2 + dx2

    x1 = x1 + dx1

#####################################

# Results

print tfmin  # 19.5
print tfmax  # 21.0

Hint: Try to find the least and greatest speeds satisfying the consitions