# Zebra For Lunch

Calculus Level 3

A crocodile is stalking a prey located 20 metres further upstream on the opposite bank of a river.

It can travel at different speeds on land and in water.

The time taken for the crocodile to reach its prey can be minimized if it swims to a particular point, $$P$$, $$x$$ metres upstream on the other side of the river as shown in the diagram above.

Let the time taken, $$T$$, measured in tenths of a second, be given by

$T(x) = 5\sqrt{36+x^2} + 4(20-x)$

Considering the times $$T$$ where $$x= 0$$ and $$x =20$$, there is a value of $$x$$ between 0 and 20 which minimizes $$T$$. If $$x=a$$ is the point at which $$T(a)$$ is minimized, find the value of $$a + T(a)$$.

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