https://file.aiquickdraw.com/mathbot/file/1727293354543l92sc1ul.jpg

Let's go through each part of the problem one by one.

### Part (a)
Colton has biked 49 miles in 3.5 hours. You are asked to find the **ratio** of distance to time, and express it as a **unit rate**.

- **Ratio**: The ratio of distance to time is simply \( \frac{49 \text{ miles}}{3.5 \text{ hours}} \).
- **Unit Rate**: To express this as a unit rate, you divide 49 by 3.5:

\[
\text{Unit rate} = \frac{49 \text{ miles}}{3.5 \text{ hours}} = 14 \text{ miles per hour}.
\]

So, Colton is biking at a **rate of 14 miles per hour**. This rate represents his **constant speed** while biking.

---

### Part (b)
In this part, Colton travels at the same rate (14 miles per hour) for 6 hours. You are asked to find the distance he would have biked after 6 hours.

Let \( d \) represent the distance.

Using the rate from part (a):

\[
\text{Distance} = \text{Rate} \times \text{Time} = 14 \text{ miles per hour} \times 6 \text{ hours} = 84 \text{ miles}.
\]

So, Colton would bike **84 miles** in 6 hours.

---

### Part (c)
Now, Colton wants to bike 200 miles. You are asked to find how many hours it will take him to bike this distance, given that he maintains the same speed of 14 miles per hour.

Let \( h \) represent the time in hours.

Set up the proportion based on the speed formula:

\[
\frac{\text{Distance}}{\text{Time}} = \text{Rate}
\]
\[
\frac{200 \text{ miles}}{h \text{ hours}} = 14 \text{ miles per hour}.
\]

Solve for \( h \):

\[
h = \frac{200}{14} \approx 14.3 \text{ hours}.
\]

So, it will take Colton approximately **14.3 hours** to bike 200 miles, which rounds to the nearest tenth as **14.3 hours**.

---

Would you like further details on any of the parts?

### Follow-up Questions:
1. What does the term "unit rate" refer to in real-world scenarios?
2. How would you set up a proportion if the time instead of the distance was unknown?
3. If Colton increased his speed to 16 miles per hour, how long would it take him to travel 200 miles?
4. How does constant speed affect proportionality in time and distance relationships?
5. How would the calculations change if Colton's speed were not constant?

### Tip:
When solving proportional problems, always ensure the units are consistent and clearly identified to avoid errors.

Colton is taking a long bike ride where he rides at a constant speed. After 3.5 hours, he has traveled a distance of 49 miles. Based on this information, you need to solve three sub-questions regarding his biking speed, distance, and time.

Solve a problem involving Colton's constant biking speed, where he covers 49 miles in 3.5 hours. Learn how to calculate unit rates, distances for different time periods, and the time required to cover specific distances. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation