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Sagot :
Let's find the average velocity for each leg of the trip and then arrange the legs from highest to lowest velocity.
The formula for average velocity [tex]\( v \)[/tex] is given by:
[tex]\[ v = \frac{d}{t} \][/tex]
where [tex]\( d \)[/tex] is the distance and [tex]\( t \)[/tex] is the time.
First, we need to convert the times given in minutes to hours because the standard unit for velocity is typically kilometers per hour (km/h).
For each leg, the conversion from minutes to hours is:
[tex]\[ \text{Time in hours} = \frac{\text{Time in minutes}}{60} \][/tex]
Let's calculate this step by step for each leg:
1. Leg A:
- Distance [tex]\( d = 18 \)[/tex] km
- Time [tex]\( t = 9 \)[/tex] minutes
- Convert time to hours: [tex]\( \frac{9}{60} = 0.15 \)[/tex] hours
- Velocity [tex]\( v_A = \frac{18}{0.15} = 120 \)[/tex] km/h
2. Leg B:
- Distance [tex]\( d = 25 \)[/tex] km
- Time [tex]\( t = 15 \)[/tex] minutes
- Convert time to hours: [tex]\( \frac{15}{60} = 0.25 \)[/tex] hours
- Velocity [tex]\( v_B = \frac{25}{0.25} = 100 \)[/tex] km/h
3. Leg C:
- Distance [tex]\( d = 24 \)[/tex] km
- Time [tex]\( t = 8 \)[/tex] minutes
- Convert time to hours: [tex]\( \frac{8}{60} = 0.1333 \)[/tex] hours
- Velocity [tex]\( v_C = \frac{24}{0.1333} \approx 180 \)[/tex] km/h
4. Leg D:
- Distance [tex]\( d = 48 \)[/tex] km
- Time [tex]\( t = 12 \)[/tex] minutes
- Convert time to hours: [tex]\( \frac{12}{60} = 0.2 \)[/tex] hours
- Velocity [tex]\( v_D = \frac{48}{0.2} = 240 \)[/tex] km/h
5. Leg E:
- Distance [tex]\( d = 15 \)[/tex] km
- Time [tex]\( t = 7 \)[/tex] minutes
- Convert time to hours: [tex]\( \frac{7}{60} \approx 0.1167 \)[/tex] hours
- Velocity [tex]\( v_E = \frac{15}{0.1167} \approx 128.57 \)[/tex] km/h
Now, we have the velocities for each leg:
- [tex]\( v_A = 120 \)[/tex] km/h
- [tex]\( v_B = 100 \)[/tex] km/h
- [tex]\( v_C = 180 \)[/tex] km/h
- [tex]\( v_D = 240 \)[/tex] km/h
- [tex]\( v_E = 128.57 \)[/tex] km/h
Let's arrange them from highest to lowest velocity:
1. Leg D: [tex]\( 240 \)[/tex] km/h
2. Leg C: [tex]\( 180 \)[/tex] km/h
3. Leg E: [tex]\( 128.57 \)[/tex] km/h
4. Leg A: [tex]\( 120 \)[/tex] km/h
5. Leg B: [tex]\( 100 \)[/tex] km/h
The formula for average velocity [tex]\( v \)[/tex] is given by:
[tex]\[ v = \frac{d}{t} \][/tex]
where [tex]\( d \)[/tex] is the distance and [tex]\( t \)[/tex] is the time.
First, we need to convert the times given in minutes to hours because the standard unit for velocity is typically kilometers per hour (km/h).
For each leg, the conversion from minutes to hours is:
[tex]\[ \text{Time in hours} = \frac{\text{Time in minutes}}{60} \][/tex]
Let's calculate this step by step for each leg:
1. Leg A:
- Distance [tex]\( d = 18 \)[/tex] km
- Time [tex]\( t = 9 \)[/tex] minutes
- Convert time to hours: [tex]\( \frac{9}{60} = 0.15 \)[/tex] hours
- Velocity [tex]\( v_A = \frac{18}{0.15} = 120 \)[/tex] km/h
2. Leg B:
- Distance [tex]\( d = 25 \)[/tex] km
- Time [tex]\( t = 15 \)[/tex] minutes
- Convert time to hours: [tex]\( \frac{15}{60} = 0.25 \)[/tex] hours
- Velocity [tex]\( v_B = \frac{25}{0.25} = 100 \)[/tex] km/h
3. Leg C:
- Distance [tex]\( d = 24 \)[/tex] km
- Time [tex]\( t = 8 \)[/tex] minutes
- Convert time to hours: [tex]\( \frac{8}{60} = 0.1333 \)[/tex] hours
- Velocity [tex]\( v_C = \frac{24}{0.1333} \approx 180 \)[/tex] km/h
4. Leg D:
- Distance [tex]\( d = 48 \)[/tex] km
- Time [tex]\( t = 12 \)[/tex] minutes
- Convert time to hours: [tex]\( \frac{12}{60} = 0.2 \)[/tex] hours
- Velocity [tex]\( v_D = \frac{48}{0.2} = 240 \)[/tex] km/h
5. Leg E:
- Distance [tex]\( d = 15 \)[/tex] km
- Time [tex]\( t = 7 \)[/tex] minutes
- Convert time to hours: [tex]\( \frac{7}{60} \approx 0.1167 \)[/tex] hours
- Velocity [tex]\( v_E = \frac{15}{0.1167} \approx 128.57 \)[/tex] km/h
Now, we have the velocities for each leg:
- [tex]\( v_A = 120 \)[/tex] km/h
- [tex]\( v_B = 100 \)[/tex] km/h
- [tex]\( v_C = 180 \)[/tex] km/h
- [tex]\( v_D = 240 \)[/tex] km/h
- [tex]\( v_E = 128.57 \)[/tex] km/h
Let's arrange them from highest to lowest velocity:
1. Leg D: [tex]\( 240 \)[/tex] km/h
2. Leg C: [tex]\( 180 \)[/tex] km/h
3. Leg E: [tex]\( 128.57 \)[/tex] km/h
4. Leg A: [tex]\( 120 \)[/tex] km/h
5. Leg B: [tex]\( 100 \)[/tex] km/h
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