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, we will define the variables and set up equations based on the information given.

### Step 1: Define Variables
Let:
- \( W \) = time taken to walk one way (in minutes)
- \( R \) = time taken to ride one way (in minutes)

### Step 2: Set Up Equations
From the problem, we have two scenarios:
1. Walking one way and riding back takes a total of 37 minutes:
\[ W + R = 37 \quad \text{(Equation 1)} \]

2. Walking both ways takes a total of 55 minutes:
\[ 2W = 55 \quad \text{(Equation 2)} \]

### Step 3: Solve for \( W \)
From Equation 2, we can find \( W \):
\[ W = \frac{55}{2} = 27.5 \text{ minutes} \]

### Step 4: Substitute \( W \) into Equation 1
Now, substitute \( W \) back into Equation 1 to find \( R \):
\[ 27.5 + R = 37 \]
\[ R = 37 - 27.5 = 9.5 \text{ minutes} \]

### Step 5: Calculate Time for Riding Both Ways
To find the time taken to ride both ways, we calculate:
\[ 2R = 2 \times 9.5 = 19 \text{ minutes} \]

### Final Answer
Thus, the time it would take to ride both ways is **19 minutes**.

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