Observe the table,

The winning times in seconds for the dash at the Olympics between and .

**a. Find the speed at which Allison is rowing and the speed of the current.**

Write equations that represent the winning times for men and women since .

Assume that both times continue along the same trend.

Consider the coordinate points are men using and :

Hence, the equation is .

Consider the coordinate points are women using and :

Hence, the equation is .

The system of equations are and .

**b.** Estimate when the womens performance will catch up to the mens performance.

** Graph:**

Graph the equations and .

Observe the table,

The womens performance will catch up to the mens performance years after .

The next Olympic year would be .

**Write prediction is not reasonable or not.**

Prediction is not reasonable.

It is unlikely that womens times will ever catch up to mens times because the times cannot continue to increase and decrease infinitely.

**a.**

The system of equations are and .

**b. **Graph of the equations and is

The next Olympic year would be .

Prediction is not reasonable.

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