Question

Carlos and Jorge have a hot dog eating contest. After the first 2 minutes, Carlos has consumed 8 hot dogs and Jorge has consumed only 7 hot dogs. From that point, Carlos eats 3 hot dogs each minute while Jorge eats 4 hot dogs per minute. After how many minutes, m, will Jorge have eaten more hot dogs than Carlos?

Answer 1

After the first 2 minutes, Jorge will have eaten more hot dogs than Carlos after just over 1 additional minute. Since they cannot eat a fraction of a hot dog, the first whole number minute when Jorge overtakes Carlos is after a total of 2 more minutes.

Step-by-step explanation:

Let's define the number of hot dogs each person has eaten after the first 2 minutes. Carlos has consumed 8 hot dogs, and Jorge has consumed 7. After the first 2 minutes, Carlos eats at a rate of 3 hot dogs per minute, while Jorge eats at a rate of 4 hot dogs per minute. To determine after how many additional minutes, m, Jorge will have eaten more hot dogs than Carlos, we can set up an equation. Let's let m represent the number of minutes after the first 2 minutes. We can express the total number of hot dogs Carlos and Jorge have eaten as follows:Carlos: 8 hot dogs + 3 hot dogs/minute × m minutes, Jorge: 7 hot dogs + 4 hot dogs/minute × m minutes. To find when Jorge will have eaten more hot dogs than Carlos, we solve for m in the inequality: 7 + 4m > 8 + 3m. First, we subtract 3m from both sides: 7 + m > 8. Now, subtract 7 from both sides: m > 1. So, after more than 1 additional minute, Jorge will have eaten more hot dogs than Carlos. Because they can't eat a fraction of a hot dog, the first whole number minute after which Jorge overtakes Carlos is after 2 minutes.