Please answer these questions

7. You must get from a point A on the straight shore of a lake to a L stranded swimmer who is at the point B in the lake. The shortest distance from B to the shore is BC = 30 m where C is a point on the shore, 40 m from you (see figure). Assume you can swim at a speed of 1 m/s and run at a speed of 4 m/s, find the point D along the shore, r meters from C, such that you can reach the swimmer - - in the minimum time? D (a) Express the running distance and swimming distance in terms of r. 40 (b) Use the result of (a) to find the time T(a) it takes for you to reach B. (c) What is a reasonable interval for a ? (d) Minimize the time T(x) over the interval specified in (c) to locate D and give an argument why it is minimum