A dog chases a rabbit. The dog is originally 600 feet away from rabbit. The dog's speed is 200 feet per minute. The rabbit's speed is 150 feet per minute. Will the dog catch the rabbit? If yes, in how many minutes?

Yes, the dog will catch the rabbit because the dog has a greater velocity than the rabbit ...

If we make two position functions, one for the rabbit and the other for the dog:

r=150t and d=200t-600

When the dog catches the rabbit, d=r so:

200t-600=150t subtract 150t from both sides

50t-600=0 add 600 to both sides

50t=600 divide both sides by 50

t=12 minutes