Final answer:
Nick and Tristan will have 11 flashcards each when Tristan catches up. It will take Tristan 99 minutes to catch up.
Step-by-step explanation:
To find out how many flashcards Nick and Tristan will have at the point when Tristan has the same number as Nick, we need to find the time it takes for Tristan to catch up. Let's say the number of flashcards they both have is x.
- Since Nick makes 4 flashcards per minute, the number of minutes he has been working is 5 / 4 = 1.25 minutes.
- Similarly, if Tristan makes 9 flashcards per minute, the number of minutes he needs to catch up is x / 9.
Setting these two equations equal to each other and solving for x:
1.25 = x / 9
x = 9 * 1.25 = 11.25
Therefore, when Tristan has 11.25 flashcards, both students will have the same number of flashcards. However, since the number of flashcards must be a whole number, we take the closest whole number to 11.25, which is 11. Therefore, both Nick and Tristan will have 11 flashcards at that point.
Now, to find out how long it will take for Tristan to have 11 flashcards:
x / 9 = 11
x = 11 * 9 = 99
Hence, it will take Tristan 99 minutes to have 11 flashcards.