A boat travels 100 miles upstream against a 10 mile/hour current. When the boat’s velocity is mile/hour, the number of gallons of gasoline consumed each hour is directly proportional to . (a) If a...

A boat travels 100 miles upstream against a 10 mile/hour current. When the boat’s velocity is mile/hour, the number of gallons of gasoline consumed each hour is directly proportional to .

(a) If a constant velocity of v mile/hour is maintained, show that the total number of y of gallons of gasoline consumed is given by

,∀ > 10 and some positive constant k.

(b) Find the speed that minimizes the number of gallons of gasoline consumed during the trip.