### Step-by-Step Solution
1. Calculate the average velocity for each leg of the trip:
To find the average velocity, we use the formula:
[tex]\[
\text{Average Velocity} = \frac{\text{Distance}}{\text{Time}} \times \frac{60}{1}
\][/tex]
The multiplication by 60 is necessary to convert the time from minutes to hours.
- Leg A:
[tex]\[
\text{Average Velocity} = \frac{15 \text{ km}}{10 \text{ min}} \times \frac{60}{1} = 90 \text{ km/h}
\][/tex]
- Leg B:
[tex]\[
\text{Average Velocity} = \frac{20 \text{ km}}{15 \text{ min}} \times \frac{60}{1} = 80 \text{ km/h}
\][/tex]
- Leg C:
[tex]\[
\text{Average Velocity} = \frac{24 \text{ km}}{12 \text{ min}} \times \frac{60}{1} = 120 \text{ km/h}
\][/tex]
- Leg D:
[tex]\[
\text{Average Velocity} = \frac{36 \text{ km}}{9 \text{ min}} \times \frac{60}{1} = 240 \text{ km/h}
\][/tex]
- Leg E:
[tex]\[
\text{Average Velocity} = \frac{14 \text{ km}}{14 \text{ min}} \times \frac{60}{1} = 60 \text{ km/h}
\][/tex]
2. Arrange the legs of the trip from the lowest velocity to the highest:
Based on the computed velocities:
- Leg E: 60 km/h
- Leg B: 80 km/h
- Leg A: 90 km/h
- Leg C: 120 km/h
- Leg D: 240 km/h
The order from the lowest velocity to the highest is:
[tex]\[
\boxed{\text{E, B, A, C, D}}
\][/tex]
