Two fishing boats depart a harbor at the same time, one traveling east, the other south. the eastbound boat travels at a speed 3 mi/h faster than the southbound boat. after 3 h the boats are 45 mi apart. find the speed of the southbound boat.

1) Let's call  the speed of the southbound boat, and  the speed of the eastbound boat, which is 3 mph faster than the southbound boat. We can write the law of motion for the two boats:



2) After a time , the two boats are  apart. Using the laws of motion written at step 1, we can write the distance the two boats covered:


The two boats travelled in perpendicular directions. Therefore, we can imagine the distance between them (45 mi) being the hypotenuse of a triangle, of which  and  are the two sides. Therefore, we can use Pythagorean theorem and write:

Solving this, we find two solutions. Discarding the negative solution, we have , which is the speed of the southbound boat.