Final answer:
Enrique drank 23/16 cups of coffee over the course of 5/2 hours. After converting the time to an improper fraction, we divide the total coffee consumed by the total time, (23/16) × (2/5) = 46/80, which simplifies to 23/40 cups per hour. None of the given options match 23/40 cups.
Step-by-step explanation:
To determine how much coffee Enrique drank each hour, we need to divide the total amount of coffee he drank by the total number of hours. He drank 23/16 cups of coffee in 21/2 hours. First, we convert 21/2 hours to an improper fraction, so it becomes 5/2 hours. Then we perform the division.
To calculate this, we take:
- Total coffee consumed: 23/16 cups
- Total time: 5/2 hours
The calculation will be (23/16) / (5/2).
To perform the division of fractions, we multiply by the reciprocal of the divisor:
(23/16) × (2/5) = (23 × 2) / (16 × 5) = 46/80
Now, we simplify the fraction:
46/80 = 23/40, which can be further reduced to 23/40 cups per hour.
So, looking at the options provided:
- A. 555/32 cups
- B. 4/5 of a cup
- C. 11/8 cups
- D. 7/8 of a cup
We find that none of these match 23/40 cups. It seems there might have been a mistake in either the question or calculation. If the calculation of 23/40 is incorrect, we should recheck our math, or if the options provided are incorrect, the question might need revision.