Ship distances woot!!?

Question

At 12 noon ship A is 45 miles due south of ship B and is sailing north at a rate of 8 miles per hour. Ship B is sailing east at a rate of 6 miles per hour.

Find the distance (d) between the ships as a function of the time (t) where t=0 represents 12:00 noon.

Determine the minimum value of d.

Please explain your processes!

Thanks

Rikou

Answer 1

distance travelled by ship A = 8t

distance travelled by ship B = 6t

d = sqrt((45 - 8t)^2 + (6t)^2)

d = sqrt(2025 - 720t + 64t^2 + 36t^2)

d = sqrt(2025 - 720t + 100t^2)

dd/dt = (1/2)(2025 - 720t + 100t^2)^(-1/2)(-720 + 200t) = 0

2025 - 720t + 100t^2 = 0

has imaginary roots

-720 + 200t = 0

t = 720/200

t = 3.6 hours

d = sqrt(2025 - 720*3.6 + 100*3.6^2)

d = 27 miles