Speed is the rate of distance over time.
The speed of the boat is 13mph south-west
Given
[tex]v_1 = 12mph[/tex] --- west
[tex]v_2 = 5mph[/tex] -- south
The speed is illustrated with the attached image
Because both speeds act at a diagonal, the speed (v) of the boat is calculated using Pythagoras theorem as follows:
[tex]v^2 = 12^2 + 5^2[/tex]
[tex]v^2 = 144 + 25[/tex]
[tex]v^2 = 169[/tex]
Take square root
[tex]v = \sqrt{169[/tex]
[tex]v = 13[/tex]
Hence, the speed of the boat is 13mph south-west
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