Kelly has finished a picnic on an island that is 200 m off shore (see figure). She wants to return to a beach house that is 600 m from the point P on the shore closest to the island. She plans to row a boat to a point on shore x meters from P and then jog along the (straight) shore to the house.

a. Let d(x) be the total length of her trip as a function of x. Find and graph this function.

b. Suppose that Kelly can row at 2 m/s and jog at 4 m/s. Let T(x) be the total time for her trip as a function of x. Find and graph y = T(x).

c. Based on your graph in part (b), estimate the point on the shore at which Kelly should land to minimize the total time of her trip. What is that minimum time?

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200 m 600 m