Francis takes a scooter on a 2-mile trip at a constant speed of 10mi/h. F(t) = 10t represents the distance traveled as a function of time. what function represents the distance remaining 

To find the function that represents the distance remaining in Francis' 2-mile trip, you can subtract the distance traveled at any given time from the total distance.

The distance traveled as a function of time is given by:
\[
F(t) = 10t
\]
where \( t \) is time in hours and \( F(t) \) is the distance traveled.

The total trip is 2 miles, so the distance remaining, \( R(t) \), is:
\[
R(t) = 2 - F(t)
\]
Substitute \( F(t) = 10t \) into the equation:
\[
R(t) = 2 - 10t
\]

Thus, the function representing the distance remaining is:
\[
R(t) = 2 - 10t
\]

### Key points:
- At \( t = 0 \), \( R(0) = 2 \) miles (the start of the trip).
- At \( t = 0.2 \) hours (12 minutes), \( R(0.2) = 0 \) miles (the trip is complete).

Would you like any more details or clarification on this?

### Related Questions:
1. How long will it take Francis to complete the 2-mile trip?
2. What is the function for time as a function of distance traveled?
3. How would the function change if Francis' speed was 12 miles per hour instead of 10?
4. What is the meaning of the slope in the function \( R(t) \)?
5. How does the trip time compare if the distance was 5 miles?

### Tip:
When modeling motion, think of the remaining distance as the total distance minus the distance already traveled—this will give you a simple linear equation in cases of constant speed.

Francis takes a scooter on a 2-mile trip at a constant speed of 10mi/h. F(t) = 10t represents the distance traveled as a function of time. What function represents the distance remaining?

Learn how to determine the remaining distance in a 2-mile trip when traveling at a constant speed of 10mi/h. This problem introduces linear functions and distance-time relationships, perfect for Grades 6-8 students. Understand the formula R(t) = 2 - 10t and calculate the distance remaining at any given time.

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