Scientists are preparing two satellites to be launched. The equation y=6800x represents the number of miles, y, that the satellite, Space Explorer A, flies in xx hours. The graph below represents the number of miles, y, that the satellite, Space Explorer B, flies in x hours.

Question

0
Hours
Miles
x
y
0
Hours
Miles
(5,23000)
(10,46000)
Space Explorer B
How much faster does Space Explorer A travel per hour than Space Explorer B?

Answer 1

To find out how much faster Space Explorer A travels per hour compared to Space Explorer B, we first need to determine the speeds of both satellites.

The equation for Space Explorer A is given as:

\[ y = 6800x \]

From this equation, we can see that the speed of Space Explorer A is 6800 miles per hour.

Next, we examine Space Explorer B, which is represented by the points (5, 23000) and (10, 46000). To determine the speed of Space Explorer B, we can calculate the distance it travels over time.

1. Calculate the speed of Space Explorer B:

   • Between 5 hours and 10 hours, the distance traveled is: \[ 46000 - 23000 = 23000 \text{ miles} \]
   • The time taken for this distance is: \[ 10 - 5 = 5 \text{ hours} \]
   • Therefore, the speed of Space Explorer B is: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{23000 \text{ miles}}{5 \text{ hours}} = 4600 \text{ miles per hour} \]

2. Find the difference in speed:

   • Now we can find out how much faster Space Explorer A is compared to Space Explorer B: \[ 6800 - 4600 = 2200 \text{ miles per hour} \]

Thus, Space Explorer A travels 2200 miles per hour faster than Space Explorer B.