A person can walk a certain distance and drive back in 6 h. He can also walk both ways in 10 h. How much time will he take to drive both ways?

Options

A. a)2h
B. b)`2 (1)/(2) h`
C. c)`6 (1)/(2) h`
D. d)`4h`

Answer

To solve the problem, we need to set up equations based on the information given.

### Step 1: Define Variables
Let:
- \( d \) = time taken to walk one way (in hours)
- \( r \) = time taken to drive one way (in hours)

### Step 2: Set Up Equations
From the problem, we have two scenarios:
1. Walking one way and driving back takes 6 hours:
\[ d + r = 6 \quad \text{(Equation 1)} \]

2. Walking both ways takes 10 hours:
\[ 2d = 10 \quad \text{(Equation 2)} \]

### Step 3: Solve Equation 2
From Equation 2, we can find \( d \):
\[ d = \frac{10}{2} = 5 \quad \text{(time taken to walk one way)} \]

### Step 4: Substitute \( d \) in Equation 1
Now substitute \( d = 5 \) into Equation 1:
\[ 5 + r = 6 \]

### Step 5: Solve for \( r \)
Now, solve for \( r \):
\[ r = 6 - 5 = 1 \quad \text{(time taken to drive one way)} \]

### Step 6: Calculate Time to Drive Both Ways
To find the time taken to drive both ways, we multiply \( r \) by 2:
\[ \text{Time to drive both ways} = 2r = 2 \times 1 = 2 \text{ hours} \]

### Final Answer
The time taken to drive both ways is **2 hours**.

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