To find the average speed of the buses, we can use the formula for speed, which is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Each student took 30 minutes to reach school. We need to convert this time into hours because speed is typically expressed in miles per hour (mi/h). Since there are 60 minutes in an hour, 30 minutes is:
\[ 30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours} \]
Now we will calculate the average speed for each bus:
-
Student who rode 8 miles: \[ \text{Speed} = \frac{8 \text{ miles}}{0.5 \text{ hours}} = 16 \text{ mi/h} \]
-
Student who rode 10 miles: \[ \text{Speed} = \frac{10 \text{ miles}}{0.5 \text{ hours}} = 20 \text{ mi/h} \]
-
Students who rode 12 miles (each): \[ \text{Speed} = \frac{12 \text{ miles}}{0.5 \text{ hours}} = 24 \text{ mi/h} \]
Now we can find the average speed of all buses by first calculating the total distance traveled and the total time taken:
-
Total distance: \[ 8 \text{ miles} + 10 \text{ miles} + 12 \text{ miles} + 12 \text{ miles} = 42 \text{ miles} \]
-
Total time: Since there are four students each taking 0.5 hours: \[ 0.5 \text{ hours} \times 4 = 2 \text{ hours} \]
Now we can calculate the overall average speed:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{42 \text{ miles}}{2 \text{ hours}} = 21 \text{ mi/h} \]
Thus, the average speed of the buses is 21 mi/h.