To find the time it takes to travel 900 miles at a speed of 30 miles per hour, you can use the following relationship based on the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Rearranging this formula to find time gives:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
In this case, the distance is 900 miles and the speed is 30 miles per hour. Substituting these values in, we have:
\[ \text{Time} = \frac{900 \text{ miles}}{30 \text{ miles per hour}} = 30 \text{ hours} \]
Now we need to set \(\frac{30 \text{ miles}}{1 \text{ hour}}\) equal to one of the given options in order to solve for time.
Using the given options, we want to match the form:
\[ \frac{\text{Distance}}{\text{Time}} = \frac{30 \text{ miles}}{\text{1 hour}} \]
The correct relationship that can be set up is:
\[ \frac{30 \text{ miles}}{1 \text{ hour}} = \frac{900 \text{ miles}}{?\text{ hours}} \]
This means that the correct answer to set it equal to is:
\(\frac{900 \text{ miles}}{? \text{ hours}}\)
To find the unknown (time), substitute the known values:
\[ \frac{30 \text{ miles}}{1 \text{ hour}} = \frac{900 \text{ miles}}{? \text{ hours}} \]
Therefore, the answer is:
\[ \text{StartFraction 900 miles Over question mark hours EndFraction} \]
This shows that you can set the speed of \( \frac{30 \text{ miles}}{1 \text{ hour}} \) equal to \( \frac{900 \text{ miles}}{? \text{ hours}} \) to find the time it takes to travel 900 miles at that speed.
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