To find the average speed of the buses, we can use the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
In this case, we need to calculate the average speed for each of the buses used by the four students. Each trip took 30 minutes, which we can convert to hours:
\[ 30 \text{ minutes} = \frac{30}{60} = 0.5 \text{ hours} \]
Next, we will calculate the speeds for each student based on their distances.
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Student who rode 8 miles: \[ \text{Speed} = \frac{8 \text{ miles}}{0.5 \text{ hours}} = 16 \text{ miles per hour} \]
-
Student who rode 10 miles: \[ \text{Speed} = \frac{10 \text{ miles}}{0.5 \text{ hours}} = 20 \text{ miles per hour} \]
-
Student who rode 12 miles (first): \[ \text{Speed} = \frac{12 \text{ miles}}{0.5 \text{ hours}} = 24 \text{ miles per hour} \]
-
Student who rode 12 miles (second): \[ \text{Speed} = \frac{12 \text{ miles}}{0.5 \text{ hours}} = 24 \text{ miles per hour} \]
Now, we have the speeds of the four students:
- 16 mph
- 20 mph
- 24 mph
- 24 mph
To calculate the average speed of the buses, we need to find the average of these speeds:
\[ \text{Average Speed} = \frac{\text{Total Speed}}{\text{Number of Students}} = \frac{16 + 20 + 24 + 24}{4} \]
Calculating the total speed:
\[ 16 + 20 + 24 + 24 = 84 \]
Now, divide by the number of students:
\[ \text{Average Speed} = \frac{84}{4} = 21 \text{ miles per hour} \]
So, the average speed of the buses was 21 miles per hour.