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**Viral** (In this question the unit vectors i and j are due east and north respectively.)

At noon a ship S is 600m due north of an observation point O and a speedboat B is 120m due north of the same point. The ship S has a constant velocity of $\displaystyle |7i+8j|ms^{-1}$ and the speedboat B has a constant velocity of $\displaystyle |7i+24j|ms^{-1}$.

b). Show that S and B will collide and find the time when this collision occurs and the position vector of the point of collision.

My attempt:

$\displaystyle 600i + t(7i+8j) = 120i + t(7i+24j)$

From there I need to find what t equals. That would give me the time when they collide. I've tried rearranging the equation to get t on one side, I've even tried finding the magnitude of the component vectors, where 7i+24j would be 25, but I just can't work it out =\ . Please tell me how to work it out, and I will go from there.