Walking and swimming A man wishes to gel from an initial point on the shore of a circular pond with radius 1 mi to a point on the shore directly opposite (on the other end of the diameter). He plans to swim from the initial point to another point on the shore and then walk along the shore to the terminal point. a. If he swims at 2 mi/hr and walks at 4 mi/hr, what are the minimum and maximum times for the trip? b. If he swims at 2 mi/hr and walks at 1.5 mi/hr, what are the minimum and maximum times for the trip? c. If he swims at 2 mi/hr, what is the minimum walking speed for which it is quickest to walk the entire distance?

Solution Step 1: Given date Radius of the circular pond,r=1mi Swimming speed,2mi/h Walking speed=4mi/h Step 2: Step 3: Here A is initial point and B is terminal point By the above diagram man first walk from A to C and swim from C to E and then again walks from E to B Step 4: Step 5: