Sure! To figure out how long it will take for Amanda and Alexis to meet, we can use the formula you provided:
\[
D = r \times t
\]
Where:
- \( D \) is distance,
- \( r \) is the rate (or speed),
- \( t \) is time.
Step 1: Find the combined rate of Amanda and Alexis
Since Amanda and Alexis are walking toward each other, we can add their speeds together to find the combined rate at which they are closing the distance between them.
- Amanda's speed: 3.5 miles per hour
- Alexis's speed: 4 miles per hour
Combined rate:
\[
\text{Combined rate} = 3.5 + 4 = 7.5 \text{ miles per hour}
\]
Step 2: Set up the equation
The total distance they have to cover to meet is the distance between their houses, which is given as 4 miles.
Now, we can use the distance formula to find the time \( t \) it takes for them to meet:
\[
D = r \times t
\]
Substituting the known values:
\[
4 = 7.5 \times t
\]
Step 3: Solve for time \( t \)
To find \( t \), we will divide both sides by the combined rate (7.5):
\[
t = \frac{4}{7.5}
\]
Step 4: Perform the division
Now, let's calculate that:
\[
t = \frac{4}{7.5} \approx 0.5333 \text{ hours}
\]
Step 5: Round to the nearest hundredth
Rounding \( 0.5333 \) to the nearest hundredth gives:
\[
t \approx 0.53 \text{ hours}
\]
Conclusion
So, it will take approximately 0.53 hours for Amanda and Alexis to meet.
Summary Steps
- Find the combined rate of both individuals.
- Use the distance formula to set up the equation.
- Solve for time by rearranging the equation.
- Calculate and round as necessary.
If you have any other questions or need further clarification, feel free to ask!
