To determine whose marble will reach the 6-foot mark faster, we first need to convert the given information into speed values for both Pete's and Stephano's marbles.
From the equation for Stephano’s marble, \( f = 2.25s \), we find that:
- The speed of Stephano’s marble is \( 2.25 \) feet per second.
To find the time it takes for Stephano’s marble to reach 6 feet, we can use the equation: \[ s = \frac{f}{\text{speed}} = \frac{6 \text{ feet}}{2.25 \text{ feet per second}} \approx 2.67 \text{ seconds} \]
Now we need to know the speed of Pete’s marble. The information in the options suggests different speeds, so we have to break them down to evaluate correctly.
Since the options provide conflicting information about the speed of Pete’s marble, let’s analyze the choices themselves:
A. Suggests Pete's marble travels at 2.25 feet/second. B. Suggests Pete’s marble travels only to 5 feet (which is irrelevant to our 6 feet question). C. States Pete's marble travels at 1.50 feet/second. D. States Stephano's marble travels faster and provides no specific speed for Pete’s.
Assuming option C, if Pete's marble travels at 1.50 feet/second, we can calculate the time for Pete’s marble to reach 6 feet: \[ s = \frac{6 \text{ feet}}{1.50 \text{ feet per second}} = 4 \text{ seconds} \]
Now we compare:
- Stephano's marble: approximately \( 2.67 \) seconds
- Pete's marble: \( 4 \) seconds
From this analysis, Stephano’s marble will reach the 6-foot mark fastest.
The correct conclusion based on the evaluations provided in the options is: C. Stephano's marble will reach 6 feet fastest because Pete's marble travels at 1.50 feet per second and Stephano's marble travels at 2.25 feet per second.
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