Partnership between A and B

Question

Two sea trawlers left a sea-port simultaneously in two mutually perpendicular directions. 30 mins later, the shortest distance between them was 17 km. And another 15 mins later, one trawler was 10.5 km further from the origin than the other. Find the speed of each trawler.

Answer 1

Let X represent the speed of the slower trawler in km/hr. Then per the 3rd sentence, the faster is traveling X+(10.5*4/3) or X+14 km/hr.

Since they are moving perpendicularly away wrt each other, the distance between them at any point would be the hypotenuse of the right triangle made by their 2 paths and the distance between them. Thus, by the 2nd sentence and the Pythagorean theorem:

17² = (X/2)² + ((X+14)/2)²

Solve for X to get the slower trawler speed and add 14 to that for the faster.