Question

scientists are preparing two satellites to be launched. the satellite, space explorer b, flies 87,000 miles in 15 hours. the graph below represents the number of miles, y, that the satellite, space explorer a, flies in x hours.

Explanation:

1. First, find the speed of Space - Explorer B:

• The speed formula is \(v=\frac{d}{t}\), where \(d\) is distance and \(t\) is time.
• For Space - Explorer B, \(d = 87000\) miles and \(t = 15\) hours.
• So, \(v_B=\frac{87000}{15}=5800\) miles per hour.

1. Then, find the speed of Space - Explorer A:

• We can use the two - point form \((x_1,y_1)=(5,41000)\) and \((x_2,y_2)=(10,82000)\) on the graph of Space - Explorer A. The speed (which is the slope of the line representing distance - time relationship) is \(v_A=\frac{y_2 - y_1}{x_2 - x_1}\).
• \(v_A=\frac{82000 - 41000}{10 - 5}=\frac{41000}{5}=8200\) miles per hour.

1. Now, compare the speeds:

• To find how much faster Space - Explorer A is than Space - Explorer B, we subtract the speed of B from the speed of A.
• \(v = v_A−v_B\).
• \(v=8200 - 5800 = 2400\) miles per hour.

Step1: Calculate speed of B

Using speed formula \(v=\frac{d}{t}\), with \(d = 87000\) and \(t = 15\), we get \(v_B=\frac{87000}{15}\).

Step2: Calculate speed of A

Using slope formula \(v=\frac{y_2 - y_1}{x_2 - x_1}\) with \((x_1,y_1)=(5,41000)\) and \((x_2,y_2)=(10,82000)\), we get \(v_A=\frac{82000 - 41000}{10 - 5}\).

Step3: Find speed difference

Subtract \(v_B\) from \(v_A\), \(v = v_A−v_B\).

Answer:

2400 miles per hour