Calculating the Time of a Trip
Two oceanfront homes are located 8 miles apart on a straight stretch of beach, each a distance of 1 mile from a paved road that parallels the ocean. Sally can jog 8 miles per hour along the paved road but only 3 miles an hour in the sand on the beach. Because of a river directly between the two houses, it is necessary to jog in the sand to the road, continue on the road, and then jog directly back in the sand to get from one house to the other. The time time T to get from one house to the other as a function of the angle theta t is given by the following:
T(t) = 1 + (2/[3 sin(t)]) - (1/[4 tan(t)]), where theta t lies between 0 degrees and 90 degrees.
Calculate the time T for theta t = 30 degrees. How long is Sally on the paved road?