Question

Jon Begins jogging at a steady 3 m/sec down the middle of lane one of a straight track. Laura starts even with him in the cneter of lane two but moves at 4 m.sec. At the instant they begin, Ellis is loacted 100 meters down the track in lane four, and is heading towards them in his at 6 m.sec. After how many seconds will the runners lie in a straight line?

a) Let t be the number of seconds the three have been running. Write expressions for the number of meters each has run after t seconds.

b) Consider the location of each runner as a point on a graph. What quantity might you use as the x-coordinate? What quantity might you use as the x-coordinate? What quantity might you use as the y-coordinate?

c) How can you tell if three points are on a line? Use this to solve the problem.

Answer 1

The runners will be in a straight line after 1/2 seconds.

To solve this problem, we can set the y-coordinates of each runner equal to each other and solve for t. The y-coordinate represents the lane number, and if the lane numbers are equal, the runners are on a straight line.

Jon: y = 1

Laura: y = 2

Ellis: y = 4

Jon: 3t = 1

Laura: 4t = 2

Ellis: 6t = 4

Solving these equations simultaneously, we find that t = 1/2 seconds. This means that after 1/2 seconds, the runners will be in a straight line.