Answer:
The rate at which both of them are moving apart is 4.9761 ft/sec.
Step-by-step explanation:
Given:
Rate at which the woman is walking,
= 3 ft/sec
Rate at which the man is walking,
= 2 ft/sec
Collective rate of both,
= 5 ft/sec
Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min = 20 min
Now,
Distance traveled by man and woman are
and
ft respectively.
⇒ 
⇒ 
As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate
.
Lets calculate h.
Applying Pythagoras formula.
⇒
⇒ 
Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.
Differentiating with respect to time.
⇒ 
⇒ 
⇒
...as 
⇒ Plugging the values.
⇒
...as
ft/sec
⇒
ft/sec
So the rate from which man and woman moving apart is 4.9761 ft/sec.