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Q3. a) A hydrofoil, on a ferry run , takes 10 minutes to overtake a vessel on parallel course 4 nautical miles ahead.

On the return journey, the hydrofoil takes 5 minutes to pass the same vessel which is still on the same course and speed, again from a distance of 4 nautical miles.

Calculate the speed of the hydrofoil and the vessel. (8)

(b) Solve the following system of equations for x and y:

2 x² - 3y² = 5

2 x - 3y = 1 (8)