I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways?

Options

A. 9.5 minutes
B. 19 minutes
C. 18 minutes
D. 20 minutes

Answer

To solve the problem step by step, let's define the variables and analyze the information given:

1. **Define Variables**:
- Let \( W \) be the time taken to walk one way.
- Let \( R \) be the time taken to ride one way.

2. **Information Given**:
- The total time taken to walk one way and ride back is 37 minutes:
\[ W + R = 37 \quad \text{(1)} \]
- The total time taken to walk both ways is 55 minutes:
\[ 2W = 55 \quad \text{(2)} \]

3. **Solve for Walking Time**:
- From equation (2), we can find \( W \):
\[ W = \frac{55}{2} = 27.5 \text{ minutes} \]

4. **Substitute \( W \) into Equation (1)**:
- Now substitute \( W \) back into equation (1):
\[ 27.5 + R = 37 \]

5. **Solve for Riding Time**:
- Rearranging the equation gives us:
\[ R = 37 - 27.5 = 9.5 \text{ minutes} \]

6. **Calculate Time for Riding Both Ways**:
- The time taken to ride both ways is:
\[ 2R = 2 \times 9.5 = 19 \text{ minutes} \]

7. **Final Answer**:
- Therefore, the time it would take to ride both ways is **19 minutes**.