Question

A ship travels from Port A north at a speed of 32 km/h for 3 h. Then it turns 90° and travels west at 30 km/h for 5.5 h. When it reaches Port B, what is the shortest distance from Port A? Express your answer to the hearest kilometre. Show ALL your work for full marks​

Answer 1

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