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.