Two ships leave a dock at the same time. One sails northeast at the rate of 8.5 miles an hour, the other sails north at the rate of 10 miles an hour. How far apart are they at the end of 2 hours?

Question

SmokeyBrown · Answer

Hi, and welcome to QuestionCove!

The first step would be to determine the distance that both ships travel during those two hours.
At a rate of 8.5 miles per hour, the first ship travels 8.5*2 miles north-east at the end of 2 hours (17 miles northeast)
At a rate of 10 miles per hour, the second ship travels 10*2 miles north at the end of 2 hours (20 miles north)
Based on this knowledge, we can imagine a triangle connecting the first ship, the second ship, and the dock, as in the picture I drew below. There are also some right triangles you could imagine, which we can use to solve the question.

We know that the first ship goes 17 miles northeast. How many miles north and how many miles east is this, relative to the dock? You can use the Pythagorean theorem (a^2+b^2=c^2) to find the answer; in this case a=b and c=17.
Once you solve that part, you can then solve for the right triangle connecting the two ships; using the Pythagorean theorem yet again, you can solve for the distance between the ships

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