To find out how long you'll have to wait for the ride with your fast pass, first convert the wait times into improper fractions.
The original wait time is \( 2 \frac{3}{4} \) hours. Converting that to an improper fraction:
- \( 2 \) hours is \( 2 \times 4 = 8 \) quarters of an hour.
- Adding \( 3 \) quarters gives \( 8 + 3 = 11 \) quarters. So, \( 2 \frac{3}{4} \) hours is \( \frac{11}{4} \) hours.
Now, the fast pass saves \( 1 \frac{1}{2} \) hours, which in fractions is:
- \( 1 \) hour is \( 1 \times 2 = 2 \) halves of an hour.
- Adding \( 1 \) half gives \( 2 + 1 = 3 \) halves. So, \( 1 \frac{1}{2} \) hours is \( \frac{3}{2} \) hours.
Now, we will subtract the saved time from the original wait time. First, we need a common denominator for the fractions \( \frac{11}{4} \) and \( \frac{3}{2} \):
- The least common denominator is \( 4 \).
Convert \( \frac{3}{2} \) to quarters:
- \( \frac{3}{2} = \frac{3 \times 2}{2 \times 2} = \frac{6}{4} \).
Now, subtract the two fractions: \[ \frac{11}{4} - \frac{6}{4} = \frac{5}{4} \]
Finally, convert \( \frac{5}{4} \) back to a mixed number:
- \( \frac{5}{4} = 1 \frac{1}{4} \).
So, after using the fast pass, you'll have to wait 1 hour and 15 minutes, or 1 1/4 hours.
Among the options provided, the correct answer is: 1 1/4 hours.
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