**Problem : **
Suppose a dog named Tika is chasing a duck in a straight line. If the duck's speed is
given by *d'*(*t*) = 5 feet per second and Tika's speed by *T'*(*t*) = 2*t* feet per second, how
far has Tika traveled when her speed is equal to the duck's speed? If the duck gets a
100 foot head start, how far has Tika traveled when she catches the duck?

Figure %: The Dog Tika Chasing a Duck

2tdt = (t^{2}|_{0}^{5/2}) = |

To find how far Tika must run to catch the duck, we must find the functions that give the distance traveled by Tika and by the duck in the first

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