To calculate the average speed of the buses, we first need to determine the total distance traveled by all the students and the total time taken.
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Distances for each student:
- Student 1: 8 miles
- Student 2: 10 miles
- Student 3: 12 miles
- Student 4: 12 miles
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Total distance: \[ \text{Total distance} = 8 + 10 + 12 + 12 = 42 \text{ miles} \]
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Total time: Each trip took 30 minutes. Since there are 4 students: \[ \text{Total time} = 30 \text{ minutes} = 0.5 \text{ hours} \]
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Average speed: The average speed is calculated by dividing the total distance by the total time: \[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{42 \text{ miles}}{0.5 \text{ hours}} = 84 \text{ mi/h} \]
However, looking at the responses provided, it seems there was an error in assumptions about the average speed of individual buses instead of total. Each bus indeed traveled at its specific speed based on the distance and time taken.
Let's clarify:
For each bus:
- Student who traveled 8 miles would have speed = \( \frac{8 \text{ miles}}{0.5 \text{ hours}} = 16 \text{ mi/h} \)
- Student who traveled 10 miles would have speed = \( \frac{10 \text{ miles}}{0.5 \text{ hours}} = 20 \text{ mi/h} \)
- Two students who traveled 12 miles would have speed = \( \frac{12 \text{ miles}}{0.5 \text{ hours}} = 24 \text{ mi/h} \) each.
To find the average speed of those individual buses: Average speeds across all four buses: \[ \text{Average speed} = \frac{16 + 20 + 24 + 24}{4} = \frac{84}{4} = 21 \text{ mi/h} \]
Thus, the average speed of the buses is 21 mi/h.