To determine how many fewer miles Space Explorer B travels in one hour compared to Space Explorer A, we need to calculate the speeds (miles per hour) of both satellites.
Space Explorer A
From the points given on the graph:
- At \(x = 0\) hours, \(y = 0\) miles
- At \(x = 5\) hours, \(y = 34000\) miles
- At \(x = 10\) hours, \(y = 68000\) miles
We can find the speed (miles per hour) of Space Explorer A by seeing how many miles it travels per hour.
Between \(x = 0\) and \(x = 10\):
- Total miles traveled: \(68000 - 0 = 68000\) miles
- Total time: \(10 - 0 = 10\) hours
The speed of Space Explorer A: \[ \text{Speed of A} = \frac{68000 \text{ miles}}{10 \text{ hours}} = 6800 \text{ miles per hour} \]
Space Explorer B
From the table given:
- \(x = 7\) hours, \(y = 15400\) miles
- \(x = 16\) hours, \(y = 35200\) miles
- \(x = 23\) hours, \(y = 50600\) miles
- \(x = 25\) hours, \(y = 55000\) miles
To find the speed for Space Explorer B, we can calculate it between the known time intervals.
Let's take the values from \(x = 16\) to \(x = 25\):
- Total miles traveled: \(55000 - 35200 = 19800\) miles
- Total time: \(25 - 16 = 9\) hours
The speed of Space Explorer B: \[ \text{Speed of B} = \frac{19800 \text{ miles}}{9 \text{ hours}} \approx 2200 \text{ miles per hour} \]
Comparing Speeds
Now, we can compare the speeds:
- Speed of A: \(6800 \text{ miles per hour}\)
- Speed of B: \(2200 \text{ miles per hour}\)
The difference in speed is: \[ \text{Difference} = 6800 - 2200 = 4600 \text{ miles per hour} \]
Conclusion
Space Explorer B travels 4600 fewer miles in one hour than Space Explorer A.