Question

Four students rode different buses to school, and each trip took 30 min . One student rode 8 mi , one rode 10 mi , and the other two each rode 12 mi . What was the average speed of the buses?(1 point) Responses 16 mi/h 16 miles per hour 21 mi/h 21 mi over h 42 mi/h 42 miles per hour 1.4 mi/h

Answer 1

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:

1. **Student who rode 8 miles:**
\[
\text{Speed} = \frac{8 \text{ miles}}{0.5 \text{ hours}} = 16 \text{ mi/h}
\]

2. **Student who rode 10 miles:**
\[
\text{Speed} = \frac{10 \text{ miles}}{0.5 \text{ hours}} = 20 \text{ mi/h}
\]

3. **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**.