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# Submarine word problem

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The movement of two submarines are being followed by a tracking system, and the positions of the submarines are modelled by points. The position of Sub A at time t is (2t+2, 2t+1) and the position of Sub B at time t is (4-t, t+5)
(distance in Kilometers)

1.How would I go about eliminating t from each pair of coordinates, and from this realise each Sub travels in a straight line?

2. How would I go about finding the distance between the Subs at each of the times t=0 and t=2?

3. If d is the distance between the pods at time t, how would I go about finding an expression for d squared in terms of t? And how would I go about completing the square for this expression, and show that the minimum value of d squared is attained when t =1?

4. And how would I go about finding the shortest distance between the Subs?

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#### Solution Preview

Time And Distances
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The movement of two submarines are being followed by a tracking system, and the positions of the submarines are modelled by points. The position of Sub A at time t is (2t+2, 2t+1) and the position of Sub B at time t is (4-t, t+5)
(distance in Kilometers)

1.How would I go about eliminating t from each pair of coordinates, and from this realise each Sub travels in a straight line?

For the Sub A, its position at time t is (2t+2, 2t+1) which tells us
...

#### Solution Summary

This shows how to work with the movement of two submarines modelled by points based on an equation.

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