Answer :
To determine which of the given speeds is the greatest, we first need to convert each speed into the same unit. We'll convert all speeds to meters per second (m/s). Here are the conversions for each given speed:
1. Speed A: [tex]\( 40 \)[/tex] miles per hour (mi/h)
- Conversion factor: [tex]\( 1 \text{ mile} = 1609 \text{ meters} \)[/tex]
- Conversion to meters per second:
[tex]\[ 40 \text{ mi/h} = 40 \times \frac{1609 \text{ m}}{1 \text{ mile}} \times \frac{1 \text{ hour}}{3600 \text{ seconds}} = 40 \times \frac{1609}{3600} \approx 17.8778 \text{ m/s} \][/tex]
2. Speed B: [tex]\( 2.0 \times 10^5 \)[/tex] millimeters per minute (mm/min)
- Conversion factors: [tex]\( 1 \text{ mm} = 0.001 \text{ meters} \)[/tex] and [tex]\( 1 \text{ minute} = 60 \text{ seconds} \)[/tex]
- Conversion to meters per second:
[tex]\[ 2.0 \times 10^5 \text{ mm/min} = 200000 \times 0.001 \text{ m} \times \frac{1 \text{ min}}{60 \text{ s}} = 200 \times \frac{1}{60} \approx 3.3333 \text{ m/s} \][/tex]
3. Speed C: [tex]\( 400 \)[/tex] meters per minute (m/min)
- Conversion factor: [tex]\( 1 \text{ minute} = 60 \text{ seconds} \)[/tex]
- Conversion to meters per second:
[tex]\[ 400 \text{ m/min} = 400 \times \frac{1 \text{ min}}{60 \text{ s}} \approx 6.6667 \text{ m/s} \][/tex]
4. Speed D: [tex]\( 0.74 \)[/tex] kilometers per minute (km/min)
- Conversion factors: [tex]\( 1 \text{ km} = 1000 \text{ meters} \)[/tex] and [tex]\( 1 \text{ minute} = 60 \text{ seconds} \)[/tex]
- Conversion to meters per second:
[tex]\[ 0.74 \text{ km/min} = 0.74 \times 1000 \text{ m} \times \frac{1 \text{ min}}{60 \text{ s}} \approx 12.3333 \text{ m/s} \][/tex]
5. Speed E: [tex]\( 40 \)[/tex] kilometers per hour (km/h)
- Conversion factors: [tex]\( 1 \text{ km} = 1000 \text{ meters} \)[/tex] and [tex]\( 1 \text{ hour} = 3600 \text{ seconds} \)[/tex]
- Conversion to meters per second:
[tex]\[ 40 \text{ km/h} = 40 \times 1000 \text{ m} \times \frac{1 \text{ hour}}{3600 \text{ s}} \approx 11.1111 \text{ m/s} \][/tex]
After converting all the speeds to meters per second, we have:
[tex]\[ \begin{align*} \text{Speed A} & \approx 17.8778 \text{ m/s} \\ \text{Speed B} & \approx 3.3333 \text{ m/s} \\ \text{Speed C} & \approx 6.6667 \text{ m/s} \\ \text{Speed D} & \approx 12.3333 \text{ m/s} \\ \text{Speed E} & \approx 11.1111 \text{ m/s} \end{align*} \][/tex]
Comparing these values, it is clear that the greatest speed is Speed A, which is approximately [tex]\( 17.8778 \)[/tex] m/s.
Therefore, the greatest speed is:
[tex]\[ \boxed{40 \text{ mi/h}} \][/tex]
1. Speed A: [tex]\( 40 \)[/tex] miles per hour (mi/h)
- Conversion factor: [tex]\( 1 \text{ mile} = 1609 \text{ meters} \)[/tex]
- Conversion to meters per second:
[tex]\[ 40 \text{ mi/h} = 40 \times \frac{1609 \text{ m}}{1 \text{ mile}} \times \frac{1 \text{ hour}}{3600 \text{ seconds}} = 40 \times \frac{1609}{3600} \approx 17.8778 \text{ m/s} \][/tex]
2. Speed B: [tex]\( 2.0 \times 10^5 \)[/tex] millimeters per minute (mm/min)
- Conversion factors: [tex]\( 1 \text{ mm} = 0.001 \text{ meters} \)[/tex] and [tex]\( 1 \text{ minute} = 60 \text{ seconds} \)[/tex]
- Conversion to meters per second:
[tex]\[ 2.0 \times 10^5 \text{ mm/min} = 200000 \times 0.001 \text{ m} \times \frac{1 \text{ min}}{60 \text{ s}} = 200 \times \frac{1}{60} \approx 3.3333 \text{ m/s} \][/tex]
3. Speed C: [tex]\( 400 \)[/tex] meters per minute (m/min)
- Conversion factor: [tex]\( 1 \text{ minute} = 60 \text{ seconds} \)[/tex]
- Conversion to meters per second:
[tex]\[ 400 \text{ m/min} = 400 \times \frac{1 \text{ min}}{60 \text{ s}} \approx 6.6667 \text{ m/s} \][/tex]
4. Speed D: [tex]\( 0.74 \)[/tex] kilometers per minute (km/min)
- Conversion factors: [tex]\( 1 \text{ km} = 1000 \text{ meters} \)[/tex] and [tex]\( 1 \text{ minute} = 60 \text{ seconds} \)[/tex]
- Conversion to meters per second:
[tex]\[ 0.74 \text{ km/min} = 0.74 \times 1000 \text{ m} \times \frac{1 \text{ min}}{60 \text{ s}} \approx 12.3333 \text{ m/s} \][/tex]
5. Speed E: [tex]\( 40 \)[/tex] kilometers per hour (km/h)
- Conversion factors: [tex]\( 1 \text{ km} = 1000 \text{ meters} \)[/tex] and [tex]\( 1 \text{ hour} = 3600 \text{ seconds} \)[/tex]
- Conversion to meters per second:
[tex]\[ 40 \text{ km/h} = 40 \times 1000 \text{ m} \times \frac{1 \text{ hour}}{3600 \text{ s}} \approx 11.1111 \text{ m/s} \][/tex]
After converting all the speeds to meters per second, we have:
[tex]\[ \begin{align*} \text{Speed A} & \approx 17.8778 \text{ m/s} \\ \text{Speed B} & \approx 3.3333 \text{ m/s} \\ \text{Speed C} & \approx 6.6667 \text{ m/s} \\ \text{Speed D} & \approx 12.3333 \text{ m/s} \\ \text{Speed E} & \approx 11.1111 \text{ m/s} \end{align*} \][/tex]
Comparing these values, it is clear that the greatest speed is Speed A, which is approximately [tex]\( 17.8778 \)[/tex] m/s.
Therefore, the greatest speed is:
[tex]\[ \boxed{40 \text{ mi/h}} \][/tex]
