Answer:
d = 200 miles
t = 1.5 hrs after start
Step-by-step explanation:
Set the origin at car a starting point.
equation for distance to car b
x = 250 - 60t
equation for distance to car a
y = 80t
distance between car a and car b
d = √((250 - 60t)² + (80t)²)
d = √(62500 - 30000t + 3600t² + 6400t²)
d = √(62500 - 30000t + 10000t²)
d = 100√(6.25 - 3t + t²)
setting the derivative to zero
0 = 100t - 150 / √(t² - 3t - 6.25)
The denominator cannot be zero, so the numerator must
0 = 100t - 150
150 = 100t
t = 1.5 hrs
d = √((250 - 60(1.5))² + (80(1.5))²)
d = √(160² + 120²)
d = 200 miles
