an airplane makes a round trip. on the out-leg there is a tailwind of 40 km/hr, while on the return the plane faces a headwind of 40km/hr. if it takes the airplane 4 hours to travel out-leg, and 5 hours to make the return, what is the speed of the airplane in still air?

a) solve this problem

b)solve the problem again, replacing 40km/hr by w, 4 hours by t1, and 5 hours by t2

c)show that the answer to part (b) is proportional to w, and that the constant of proportionality is a function of r=t1/t2

d)graph the answer to part (b) as a function of r (from part (c)), with w=40km/hr and relate the graph to the problem as much as possible. What are the asymptotes, and what do they mean in the original problem?What of the graph is relevant to the original problem ( i.e., what is the domain of r in the original problem)?