Question

space explorer a
hours (x) miles (y)
7 23800
12 40800
17 57800
22 74800
use the dropdown menu and answer - blank below to form a true statement.
answer attempt 1 out of 2
space explorer a travels
□ miles
more
less
than space explorer b in one hour.

Explanation:

Step1: Find the rate of Space Explorer A

To find the rate (miles per hour) of Space Explorer A, we can use the formula for slope (rate) between two points \((x_1,y_1)\) and \((x_2,y_2)\), which is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Let's take the first two points \((7,23800)\) and \((12,40800)\).

$$ m=\frac{40800 - 23800}{12 - 7}=\frac{17000}{5} = 3400 $$

We can check with another pair, say \((12,40800)\) and \((17,57800)\):

$$ m=\frac{57800 - 40800}{17 - 12}=\frac{17000}{5}=3400 $$

So the rate of Space Explorer A is 3400 miles per hour. (Assuming we need to compare with a typical or given rate of Space Explorer B, but since the problem is about the rate of A, we found it as 3400. If we assume Space Explorer B has a different rate, but here we just calculate A's rate. Wait, maybe the problem expects us to find the unit rate of A, which is 3400. So if we assume that maybe B has a different rate, but since the dropdown is more or less, and we need to fill the number. Wait, maybe the original problem (maybe in the context) has Space Explorer B's rate, but since it's not given here, but from the table, we can see that the rate of A is 3400. Let's confirm with the last pair: \((17,57800)\) and \((22,74800)\):

$$ m=\frac{74800 - 57800}{22 - 17}=\frac{17000}{5}=3400 $$

So the rate of A is 3400 miles per hour. So if we assume that maybe B has a rate less than 3400, but the problem is to fill the number (3400) and the dropdown. Wait, the problem says "Space Explorer A travels [blank] miles [more/less] than Space Explorer B in one hour." So we need to find the unit rate of A, which is 3400. So the blank should be 3400, and then depending on B's rate, but since we calculated A's rate as 3400, let's proceed.

Step2: Determine the number and the comparison

Since we found that Space Explorer A's rate is 3400 miles per hour. So the number in the blank is 3400, and if we assume (maybe in the original problem context) that B's rate is less than 3400, then it's "more", but the key is the number is 3400.

Answer:

3400 (and the dropdown would be "more" if B's rate is less than 3400, but the number is 3400)