
Answer:
D(t) = 50 -2t
At 25 seconds, the dog caught up with the cat
Step-by-step explanation:
At initial time t0
Distance = 50 ft
The dog is running 12 feet per second and the cat is running 10 feet per second.
So for each each time in seconds
Dog covers 12 feet while cat extends by 10 ft .
The distance between them at any given time
D(t)= 50 +10t -12t
D(t) = 50 -2t
The time it will take the dig to get to the cat is what D= 0
D(t) = 50 -2t
0= 50- 2t
2t= 50
t= 25
So at 25 seconds, the dog caught up with the cat