Question

Scientists are preparing two satellites to be launched. The graph below represents the number of miles, yy, that the satellite, Space Explorer A, flies in xx hours.
0
Hours
Miles
x
y
0
Hours
Miles
(5,34000)
(10,68000)
Space Explorer A
The table below represents the number of miles, yy, that the satellite, Space Explorer B, flies in xx hours.
Space Explorer B
Hours left parenthesis x right parenthesisHours (x) Miles left parenthesis y right parenthesisMiles (y)
77 1540015400
16 35200
23 50600
25 55000
How many fewer miles does Space Explorer B travel in one hour than Space Explorer A?

Answer 1

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.