During their daily training race, Carl has to stop to tie his shoes . Melissa, whose shoes are Velcro , continues to run and gets 20 feet ahead of Carl . Melissa is running at a constant rate of 8 feet per second , and Carl starts running at a constant rate of 9.2 feet per second to catch up to Melissa . Which of the following equations , when solved for s, gives the number of seconds Carl will take to catch up to Melissa ?

Options

A. 8s+20=9.2s
B. 8s-20=9.2s
C. `(20+9.2s)/9.2=8s`
D. 8s=20

Answer

To solve the problem of how long it will take Carl to catch up to Melissa, we can use the distance formula, which states that distance (D) is equal to rate (R) multiplied by time (T).

### Step-by-Step Solution:

1. **Identify the Variables**:
- Let \( s \) be the time in seconds that Carl takes to catch up to Melissa.
- Melissa's speed is 8 feet per second.
- Carl's speed is 9.2 feet per second.
- Melissa has a 20-foot head start.

2. **Write the Distance Formula for Both Runners**:
- The distance Carl runs in time \( s \) is given by:
\[ D_C = \text{Rate of Carl} \times \text{Time} = 9.2s \]
- The distance Melissa runs in the same time \( s \) plus her head start is:
\[ D_M = \text{Rate of Melissa} \times \text{Time} + \text{Head Start} = 8s + 20 \]

3. **Set the Distances Equal**:
- Since both distances are equal when Carl catches up to Melissa, we can set the two equations equal to each other:
\[ 9.2s = 8s + 20 \]

4. **Rearrange the Equation**:
- To isolate \( s \), we can subtract \( 8s \) from both sides:
\[ 9.2s - 8s = 20 \]
- This simplifies to:
\[ 1.2s = 20 \]

5. **Solve for \( s \)**:
- Now, divide both sides by 1.2 to find \( s \):
\[ s = \frac{20}{1.2} \]

6. **Final Equation**:
- The equation we derived from the problem that gives the time \( s \) is:
\[ 8s + 20 = 9.2s \]

### Conclusion:
The correct equation that gives the number of seconds Carl will take to catch up to Melissa is:
\[ 8s + 20 = 9.2s \]