To calculate the average speed of the buses, we can use the formula for speed, which is:
\[ \text{speed} = \frac{\text{distance}}{\text{time}} \]
Given that each trip took 30 minutes, we first need to convert that time into hours since speed is typically expressed in miles per hour (mph).
\[ 30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours} \]
Next, we can calculate the speed for each of the distances traveled by the four students:
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For the student who rode 8 miles: \[ \text{Speed} = \frac{8 \text{ miles}}{0.5 \text{ hours}} = 16 \text{ mph} \]
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For the student who rode 10 miles: \[ \text{Speed} = \frac{10 \text{ miles}}{0.5 \text{ hours}} = 20 \text{ mph} \]
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For the first student who rode 12 miles: \[ \text{Speed} = \frac{12 \text{ miles}}{0.5 \text{ hours}} = 24 \text{ mph} \]
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For the second student who rode 12 miles: \[ \text{Speed} = \frac{12 \text{ miles}}{0.5 \text{ hours}} = 24 \text{ mph} \]
Now we have the speeds for all four students:
- 16 mph
- 20 mph
- 24 mph
- 24 mph
To find the average speed of the buses, we can sum these speeds and then divide by the number of students:
\[ \text{Average Speed} = \frac{16 + 20 + 24 + 24}{4} = \frac{84}{4} = 21 \text{ mph} \]
Thus, the average speed of the buses is 21 mph.