A man walking from a point  towards the north at a speed of  ft/s.

After five minutes a woman starts walking towards south at a speed of  ft/s.

The woman is 500 ft away from the point  towards east.

Diagram of the situation at any time  :

Assume that the man reaches some point .

Distance covered by him is  ft at  sec.

Assume that the woman starts from a point  and reaches some point .

Distance covered by the woman is  ft at  sec.

Speed of the man  ft/s.

Speed of the woman  ft/s.

Point  is 500 ft apart from the point .

Thus, .

From the figure,

.

Assume that distance between two people after time  as  ft.

And .

Apply Pythagorean theorem to the .

.

.

Differentiate on each side with respect to .

Determine the rate at which the people are moving apart after  min woman starts walking.

Woman starts walking  min later the man starts.

Thus, if the woman walks for  mins then the man walks for  mins.

Find the distance traveled by the man after  min.

.

.

Substitute  and  in above expression. 

Find the distance traveled by the woman after 15 min: 

.

Substitute  and  in above expression.

Sum of the distance travelled by man and women is .

Find distance between the people:

Consider .

Substitute  in .

.

Substitute   , and  in .

Therefore rate at which the people are moving apart after  min woman starts walking is  ft/sec. 

Rate at which the people are moving apart after  min woman starts walking is  ft/sec.