Question

Scientists are preparing two satellites to be launched. The equation y = 4600x represents the number of miles, y, that the satellite, Space Explorer A, flies in x. The Table below represents the number of miles, y, that the satellite, Space Explorer B, flies in x hours.Hours (x) Miles (y)5 1500020 6000022 6600024 72000How many fewer miles does Space Explorer B travel in one hour than Space Explorer A?

Answer 1

Space Explorer B travels 1600 fewer miles in one hour than Space Explorer A. This is calculated by determining that Space Explorer B travels 3000 miles per hour as compared to Space Explorer A's 4600 miles per hour.

Step-by-step explanation:

To determine how many fewer miles Space Explorer B travels in one hour than Space Explorer A, we first need to find the distance Space Explorer B travels in one hour. According to the table provided in the question, the distance traveled by Space Explorer B in 5 hours is 15,000 miles. We can calculate the hourly distance by dividing this number by 5 hours.

(15,000 miles) / (5 hours) = 3,000 miles per hour for Space Explorer B
Now, using the equation given for Space Explorer A, y = 4600x, we find that Space Explorer A travels 4600 miles in one hour (since x = 1). Therefore, the difference in distance traveled in one hour by the two satellites can be found by subtracting the hourly distance of Space Explorer B from that of Space Explorer A:

(4600 miles for Space Explorer A) - (3000 miles for Space Explorer B) = 1600 miles
Space Explorer B travels 1600 fewer miles in one hour than Space Explorer A.

Answer 2

Answer: We have a linear equation that represents the number of miles that satellite A flies in one hour, which is:

(A)

`y(x)=4600x`

So, In one hour this satellite flies:

`y(1)=4600(1)=4600\text{ miles}`

(B)

The linear equation for satellite B can be extracted from the given table as follows:

Slope:

`\begin{gathered} y_B(x)=mx+b \\ \rightarrow\therefore\rightarrow \\ m=(\Delta y)/(\Delta x)=(60,000-15,000)/(20-5)=(45,000)/(15)=3000 \\ \end{gathered}`

Y-Intercept:

`\begin{gathered} y_B(x)=mx+b \\ \rightarrow\therefore\rightarrow \\ y_B(5)=3000(5)+b=15,000 \\ \rightarrow\therefore\rightarrow b=15,000-36,000=-21,000 \\ \\ \therefore\rightarrow \\ y_B(x)=3000x-21,000 \end{gathered}`

Miles, that the Satellite (B) travels in one hour are:

`y_B(1)=3000(1)-21,000=3000-21,000=-18,000`

The difference in the miles traveled by these two space explorers are:

`y_B(1)-y_A(1)=-18,000mi-3000mi=-15,000`

Therefore this is the answer

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