Rob and Jill are running in straight paths with constant velocity. We know Rob i

Question

Rob and Jill are running in straight paths with constant velocity. We know Rob is at (-5, -4) at 12:00 pm, and at (7, 5) at 12:10 pm. Jill starts at (-4, 5) at 12:00 pm, and at (3, -6) at 12:10 pm. Will they meet? If not, how close will they come and If so what time during the 10 minute? Graph the runners' progress and show a table of values for every 5 seconds after 12:00. Also, determine what parametric equations would represent each runner's progress and demonstrate algebraically whether they meet or not.

Explanation / Answer

Rob:
X = -5 + (12/10)T
Y= -4 + (9/10)T
Jill:
X = -4 + (7/10)T
Y= 5 - (11/10)T
While substituting each x and y equations equating each other, gives

T=2 for the x-equations and

T=4.5 for the y-equations.

So there is no time when they occupy the same point. They do not meet.

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