'''
    lifeguard at the beach problem
    y distance to swimmer 20, x-distance 30. 
    ratio of speeds 3.
'''
import numpy as np, matplotlib.pyplot as plt
#plt.interactive(True)
s = 3
N = 1000000 
d = np.linspace(20,30,N)
t = 99.
for x in d:
    prev_t = t
    t = np.sqrt(x*x+100)/3 + np.sqrt((30-x)**2 + 100)
    if (t > prev_t): 
        print("found minimum time =",t,"  at x=",x)
        break