Which rate can you set StartFraction 30 miles Over 1 hour EndFraction equal to in order to find the time it takes to travel 900 miles at 30 miles per hour?

StartFraction question mark hours Over 900 miles EndFraction
StartFraction question mark hours Over 30 miles EndFraction
StartFraction 30 miles Over question mark hours EndFraction
StartFraction 900 miles Over question mark hours EndFraction

1 answer

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.