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Adam takes a bus on a school field trip. The bus route is split into the five legs listed in the table. Find the average velocity for each leg of the trip. Then arrange the legs of the trip from highest velocity to lowest.

\begin{tabular}{|l|l|l|}
\hline
Leg & Distance [tex]$(km)$[/tex] & Time (min) \\
\hline
A & 18 & 9 \\
\hline
B & 25 & 15 \\
\hline
C & 24 & 8 \\
\hline
D & 48 & 12 \\
\hline
E & 15 & 7 \\
\hline
\end{tabular}

[tex]\[
\begin{aligned}
&\text{Leg A} \\
&\text{Leg B} \\
&\text{Leg C} \\
&\text{Leg D} \\
&\text{Leg E}
\end{aligned}
\][/tex]

Sagot :

GinnyAnsweridn
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
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