A thirsty soldier out on a survival exercise is at point P on a straight track through the desert. She desperately wants to reach a waterhole at point W. She can walk at 8 km/h along the track, but only at 3 km/h through the soft sand off the track. Determine, using the steps below, how far along the track from P she should walk before setting off in a straight line for the waterhole, so that she reaches the waterhole in minimum time. A) Define suitable variables and units n = distance on track (KM) desert W ?=g in track ->change 2 2 km 3km/ n * 3 km 8km/h > 3-m T= time spent on track (n) B) Derive an equation for the quantity to be minimized, remembering that time = distance/speed. पू T= 1/8 + == M 8 T √(3-0)4 3 = C) Determine a sensible domain for the independent variable and explain why it is sensible. [0,3]. -> all the distare possible. D) Draw a sketch of the function in (B) with this domain and a suitable range for the dependent variable. (Use your T184 to help with this) 0.991