Final answer:
To determine when Gavin and Gibson will have the same number of tokens, we set up an equation with their respective token counts over time, which yielded an answer of 1.9 hours. However, this is not an available option, suggesting there might be an error in the question or the options provided.
Step-by-step explanation:
The question is asking when Gavin and Gibson will have the same number of tokens if Gavin starts with 50 tokens and spends them on roller coaster rides at a rate of 3 rides per hour, and Gibson starts with 12 tokens and finds 2 more on the ground every hour, with each ride costing 6 tokens.
To solve this, we need to calculate the tokens for Gavin and Gibson separately over time and find out after how many hours their remaining tokens are equal. For Gavin, the number of tokens he utilizes per hour is 3 rides × 6 tokens/ride = 18 tokens per hour. His token count reduces by this amount each hour. For Gibson, his token count increases by 2 tokens per hour as he finds more on the ground.
Let's denote the number of hours with 'h'. The equation for Gavin's remaining tokens will be 50 - 18h and for Gibson it will be 12 + 2h. To find out after how many hours they have the same number of tokens, we set the two expressions equal to each other:
50 - 18h = 12 + 2h
50 - 12 = 18h + 2h
38 = 20h
h = 38 ÷ 20
h = 1.9
Since we cannot have a fraction of an hour in the context of this question (tokens are found or spent in whole numbers), the closest whole number of hours is 2 hours. However, none of the provided options (a) 5 hours, (b) 6 hours, (c) 7 hours, (d) 8 hours, matches the calculated value of 2 hours. Based on the calculated value of 1.9 hours, there may be an error in the question or the options provided.