Answer: the shortest distance from Port A to Port B is approximately 191 kilometers.
Explanation:
We can solve this problem using the Pythagorean theorem.
Let d be the shortest distance from Port A to Port B, and let x be the distance traveled by the ship in the north direction. Then the distance traveled in the west direction is (d^2 - x^2)^(1/2).
We know that the ship travels at a speed of 32 km/h for 3 hours in the north direction, so x = 32 km/h * 3 h = 96 km. We also know that the ship travels at a speed of 30 km/h for 5.5 hours in the west direction, so (d^2 - x^2)^(1/2) = 30 km/h * 5.5 h = 165 km.
Solving for d, we have:
d^2 = x^2 + (d^2 - x^2)
d^2 = x^2 + (d^2 - x^2)
d^2 = x^2 + d^2 - x^2
d^2 = d^2
Therefore, the equation is satisfied for any value of d. However, we know that d is the shortest distance from Port A to Port B, so we take the positive square root:
d = sqrt(x^2 + (d^2 - x^2))
d = sqrt(96^2 + 165^2)
d ≈ 191 km