January 2023 Algebra 1 Regents, Part IV

This exam was adminstered in January 2023. These answers were not posted until they were unlocked on the NY Regents website or were posted elsewhere on the web.

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January 2023

Part IV: A correct answer will receive 6 credits. Partial credit can be earned.


37. Aidan and his sister Ella are having a race. Aidan runs at a rate of 10 feet per second. Ella runs at a rate of 6 feet per second. Since Ella is younger, Aidan is letting her begin 30 feet ahead of the starting line.

Let y represent the distance from the starting line and x represent the time elapsed, in seconds.

Write an equation to model the distance Aidan traveled.

Write an equation to model the distance Ella traveled.

On the set of axes below, graph your equations.

Exactly how many seconds does it take Aidan to catch up to Ella? Justify your answer.

Answer:

Take each question one at a time. Any mistakes made can only be penalized once if you carry the error through to the end.

Aiden runs at 10 ft/sec, so the distance he travels is y = 10x.

Ella runs at 6 ft/sec, but has a 30 ft head start, so the distance she travels is y = 6x + 30.

The graph will look like the one below. Make sure you label at least one line. You'll notice that the lines do not intersect at wrong numbers. Don't get thrown off by that.

Since the lines cross between 6 and 7, it's better to solve it algebraically.

10x = 6x + 30
4x = 30
x = 7.5

At x = 7.5 seconds, Aiden ran 10(7.5) = 75 feet and Ella ran 6(7.5) + 30 = 75 feet.

End of Part Exam

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