A spider is located at the position (1,2) in a coordinate system, where the units on each axis are feet. An ant is located at the position (15,0) in the same coordinate system. Assume the location of the spider after t minutes is s(t) = (1 + 2t,2 + t) and the location of the ant after t minutes is a(t) = (15 2t,2t).

(a) Sketch a picture of the situation, indicating the locations of the spider and ant at times t = 0,1,2,3,4,5 minutes. Label the locations of the bugs in your picture, using the notation s(0), s(1),...,s(5), a(0), a(1), ..., a(5).

(b) When will the x-coordinate of the spider equal 5? When will the y-coordinate of the ant equal 5?

(c) Where is the spider located when its y-coordinate is 3?

(d) Where is each bug located when the y-coordinate of the spider is twice as large as the y-coordinate of the ant?

(e) How far apart are the bugs when their x-coordinates coincide? Draw a picture, indicating the locations of each bug when their x-coordinates coincide.

(f) A sugar cube is located at the position (9,6). Explain why each bug will pass through the position of the sugar cube. Which bug reaches the sugar cube first?

(g) Find the speed of each bug along its line of motion; which bug is moving faster?