# JOMO 6, Short 5

Geometry Level 3

A man was standing on the top of a $$300 \text{m}$$ tall tower on coast of Arabic sea. He saw a ship in the sea which was coming towards the coast with a uniform velocity. The angle of depression with which he had to see the ship was $$30^{\circ}$$. After 40 seconds that angle of depression was seen to be $$45^{\circ}$$. Let the speed of the ship be $$x$$ m/s. The ship needs $$y$$ seconds more to reach the coast from the current point . Then the value of $$x + y$$ can be expressed as $$\frac{a\sqrt{3} +b}{c}$$ where $$c$$ is a prime number . Find the value of $$a+b+c$$.

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