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
1616 3520035200
2323 5060050600
2525 5500055000
How many fewer miles does Space Explorer B travel in one hour than Space Explorer A?

Answer 1

To find out how many fewer miles Space Explorer B travels in one hour than Space Explorer A, we first need to determine the speeds (miles per hour) for each satellite.

### For Space Explorer A:
From the graph, we can see that:

- At **5 hours**, Space Explorer A travels **34,000 miles**.
- At **10 hours**, Space Explorer A travels **68,000 miles**.

To find the speed of Space Explorer A, we can calculate the distance per hour:

1. **Distance traveled from 5 to 10 hours:**
\[
68,000 - 34,000 = 34,000 \text{ miles}
\]

2. **Time taken:**
\[
10 - 5 = 5 \text{ hours}
\]

3. **Speed of Space Explorer A:**
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{34,000 \text{ miles}}{5 \text{ hours}} = 6,800 \text{ miles per hour}
\]

### For Space Explorer B:
Using the provided table, we can calculate the speed of Space Explorer B for different time intervals:

- From **0 to 7 hours**:
\[
\text{Distance} = 1,5400 \text{ miles}
\]
\[
\text{Speed} = \frac{15400 \text{ miles}}{7 \text{ hours}} = 2,200 \text{ miles per hour}
\]

- From **7 to 16 hours**:
\[
\text{Distance} = 35,200 - 15,400 = 20,800 \text{ miles}
\]
\[
\text{Speed} = \frac{20,800 \text{ miles}}{9 \text{ hours}} \approx 2,311.11 \text{ miles per hour}
\]

- From **16 to 23 hours**:
\[
\text{Distance} = 50,600 - 35,200 = 15,400 \text{ miles}
\]
\[
\text{Speed} = \frac{15,400 \text{ miles}}{7 \text{ hours}} \approx 2,200 \text{ miles per hour}
\]

- From **23 to 25 hours**:
\[
\text{Distance} = 55,000 - 50,600 = 4,400 \text{ miles}
\]
\[
\text{Speed} = \frac{4,400 \text{ miles}}{2 \text{ hours}} = 2,200 \text{ miles per hour}
\]

### Comparing Speeds:
The average speed of Space Explorer B ranges from **2,200 to approximately 2,311.11 miles per hour**.

### Conclusion:
Now we can find out how many fewer miles Space Explorer B travels in one hour than Space Explorer A.

1. **Space Explorer A speed**: **6,800 miles/hour**
2. **Space Explorer B speed**: **2,200 miles/hour** (using the first average for simplicity)

**Difference**:
\[
6,800 - 2,200 = 4,600 \text{ miles}
\]

Thus, Space Explorer B travels **4,600 fewer miles** than Space Explorer A in one hour.