To find out how much faster Space Explorer B travels per hour than Space Explorer A, we need to calculate the speeds of both satellites.
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Speed of Space Explorer B: The equation for Space Explorer B is given as \( y = 4600x \). This means that Space Explorer B travels at a constant speed of 4600 miles per hour (since the coefficient of \( x \) represents the speed).
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Speed of Space Explorer A: To find the speed of Space Explorer A, we can calculate the speed using the miles and hours from the table. The speed can be found by taking the total miles traveled divided by the total hours for each entry in the table.
Let's calculate the speed for Space Explorer A for each entry in the table:
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For \( x = 16 \) hours: \[ \text{Speed} = \frac{12800 \text{ miles}}{16 \text{ hours}} = 800 \text{ miles per hour} \]
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For \( x = 19 \) hours: \[ \text{Speed} = \frac{15200 \text{ miles}}{19 \text{ hours}} \approx 800 \text{ miles per hour} \]
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For \( x = 21 \) hours: \[ \text{Speed} = \frac{16800 \text{ miles}}{21 \text{ hours}} = 800 \text{ miles per hour} \]
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For \( x = 24 \) hours: \[ \text{Speed} = \frac{19200 \text{ miles}}{24 \text{ hours}} = 800 \text{ miles per hour} \]
From the calculations, we see that Space Explorer A consistently travels at 800 miles per hour.
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Comparison of speeds: Now we compare the speeds of both satellites:
- Speed of Space Explorer B = 4600 miles per hour
- Speed of Space Explorer A = 800 miles per hour
To find out how much faster Space Explorer B is traveling than Space Explorer A, we subtract the speed of Space Explorer A from the speed of Space Explorer B: \[ \text{Difference} = \text{Speed of B} - \text{Speed of A} = 4600 \text{ miles/hour} - 800 \text{ miles/hour} = 3800 \text{ miles/hour} \]
Therefore, Space Explorer B travels 3800 miles per hour faster than Space Explorer A.
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