High School

In a reading contest, Don gives Matt a 69-page head start. After [tex]t[/tex] seconds, Matt reads [tex]6t + 69[/tex] pages from the first page, and Don reads [tex]7t[/tex] pages from the first page. How far ahead of Don is Matt after [tex]t[/tex] seconds?

A. [tex]13t[/tex]
B. [tex]6t[/tex]
C. 69 pages
D. [tex]7t - 69[/tex]

Answer :

Final answer:

Matt is ahead of Don by 69 - t pages at any time t seconds into the reading contest. The correct option, phrased as 7t - 69, is misleading since it should represent the lead as 69 - t pages.

Explanation:

To determine how far ahead of Don, Matt is at any time t seconds into the reading contest, we calculate the number of pages each reader has completed. Remember, Don gives Matt a 69-page head start.

  • Matt reads 6t + 69 pages after t seconds.
  • Don reads 7t pages after t seconds.

To find the difference in pages read between Matt and Don after t seconds, we subtract the total pages read by Don from the total pages read by Matt:

Matt's progress - Don's progress = (6t + 69) - (7t) = 69 - t

Therefore, Matt is ahead by 69 - t pages.

The correct answer is d. 7t - 69, although this is phrased incorrectly. The actual calculation shows that Matt leads by 69 - t pages after t seconds, assuming you are looking for the number of pages by which Matt is ahead, not the number by which he is behind.