Question
Andre rode his bike at a constant speed. He rode 1 mile in 5 minutes.
Which of these equations represents the amount of time t (in minutes) that it takes him to ride a distance of d miles?
Which of these equations represents the amount of time t (in minutes) that it takes him to ride a distance of d miles?
Answers
GPT-4o mini
To determine the equation that represents the relationship between distance \( d \) (in miles) and time \( t \) (in minutes) for Andre's biking speed, we start with the fact that he rides 1 mile in 5 minutes. This means his speed can be expressed as:
\[
\text{Speed} = \frac{1 \text{ mile}}{5 \text{ minutes}} = \frac{1}{5} \text{ miles per minute}.
\]
To find the time \( t \) it takes him to ride \( d \) miles, we can set up the relationship between distance, speed, and time using the formula:
\[
\text{Distance} = \text{Speed} \times \text{Time}.
\]
Substituting in the values, we have:
\[
d = \left(\frac{1}{5}\right)t.
\]
To solve for time \( t \), we can rearrange the equation:
\[
t = d \times 5.
\]
Thus, the equation representing the amount of time \( t \) in minutes that it takes him to ride a distance of \( d \) miles is:
\[
t = 5d.
\]
This means for every mile \( d \) that Andre rides, it takes him \( 5d \) minutes.
\[
\text{Speed} = \frac{1 \text{ mile}}{5 \text{ minutes}} = \frac{1}{5} \text{ miles per minute}.
\]
To find the time \( t \) it takes him to ride \( d \) miles, we can set up the relationship between distance, speed, and time using the formula:
\[
\text{Distance} = \text{Speed} \times \text{Time}.
\]
Substituting in the values, we have:
\[
d = \left(\frac{1}{5}\right)t.
\]
To solve for time \( t \), we can rearrange the equation:
\[
t = d \times 5.
\]
Thus, the equation representing the amount of time \( t \) in minutes that it takes him to ride a distance of \( d \) miles is:
\[
t = 5d.
\]
This means for every mile \( d \) that Andre rides, it takes him \( 5d \) minutes.