In Exercises 40 through 49, assume that the required extreme value is a relative extremum.

Tom, Dick, and Mary are participating in a cross-country relay race. Tom will trudge as fast as he can through thick woods to the edge of a river. Then Dick will take over and row to the opposite shore, where Mary will take the baton and run along the river road to the finish line. The course is shown in the accompanying figure. Teams must start at point S and finish at F, but they may position one member anywhere along the shore of the river and another anywhere along the river road.

a. Suppose Tom can trudge at 2 mph; Dick can row at 4 mph; and Mary can run at 6 mph. Where should Dick and Mary receive the baton for the team to finish the course as quickly as possible?

b. The main competition for Tom, Dick, and Mary is the team of Nan, Fran, and Phineas. If Nan can trudge at 1.7 mph, Fran can row at 3.5 mph, and Phineas can run at 6.3 mph, which team should win? By how much time?

Transcribed Image Text:

2.5 mi 1.2 mi Road River I Woods 1 1 T X Tom, S(0, 0) 4.3 mi Dick y Mary Lin u ww F(4.3, 3.7) www