# Some discussion points about the tables

What can you say about the position of the insects when the (x,y) coordinates in each table match? *That is when the tie occurs.*

How do their positions before and after this point change?

When do you think the tie occurs?

*In this case, from the start of the race until 7 minutes, Arnie is ahead. The lead narrows until at 8 seconds Sally is now ahead, but by only .25 feet. So, sometime before seven seconds, the tie occurs.*

To be more precise, you might use interpolation and guess and check to try and infer the time of the tie, (this can be quite time consuming.) Whatever your method, make your best guess (and use the equations to verify).

Closer to 7 minutes than 6, so (6.6, 8.3) might fit here

*You might try to use interpolation and/or guess and check to infer the time of the tie **(this can be quite time consuming.) Whatever your method, make your best guess.*

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