Question

Four students rode different buses to school and each trip took 30 minutes one student rode 8 miles one rode 10 miles and the other two each rode 12 miles what was the average speed of the buses

Answer 1

To calculate the average speed for each student, we can use the formula for speed:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

We're given that each trip took 30 minutes, which we can convert to hours for the calculation:

\[
30 \text{ minutes} = \frac{30}{60} = 0.5 \text{ hours}
\]

Now we can calculate the average speed for each distance:

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

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

3. For the students who each rode 12 miles:
\[
\text{Speed} = \frac{12 \text{ miles}}{0.5 \text{ hours}} = 24 \text{ miles per hour}
\]
(This is the same for both students who rode 12 miles.)

Now, we can calculate the average speed of all four buses. To do this, we'll find the total distance and total time:

- Total distance:
\[
8 + 10 + 12 + 12 = 42 \text{ miles}
\]

- Total time (for 4 students, each with a trip of 0.5 hours):
\[
0.5 + 0.5 + 0.5 + 0.5 = 2 \text{ hours}
\]

Now we can find the overall average speed:

\[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{42 \text{ miles}}{2 \text{ hours}} = 21 \text{ miles per hour}
\]

Thus, the average speed of the buses is **21 miles per hour**.