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

Answer 1

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.

1. Student who rode 8 miles:
\[
\text{Speed} = \frac{8 \text{ miles}}{0.5 \text{ hours}} = 16 \text{ miles per hour}
\]

2. Student who rode 10 miles:
\[
\text{Speed} = \frac{10 \text{ miles}}{0.5 \text{ hours}} = 20 \text{ miles per hour}
\]

3. Student who rode 12 miles (first):
\[
\text{Speed} = \frac{12 \text{ miles}}{0.5 \text{ hours}} = 24 \text{ miles per hour}
\]

4. 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**.