# Science:Math Exam Resources/Courses/MATH100/December 2018/Question 06/Solution 1

Let be the distance from the origin to the particle and let be the distance from the origin to the particle . Also Let be the distance between and . Notice that and are functions of time and we shall thus write them as respectively.

By the given information, we have units/min and units/min. Using the initial positions, then we see that and . We can relate these two functions by Pythagoras' theorem: we have , and therefore

Now, we will first determine the time at which the distance between the particles is units. We do this by setting and solving for . This gives

and therefore (we can ignore the negative root since time cannot be negative).

Next, we want to find when . By differentiating both sides of the equation , we get . Now we can plug in and , which gives .