A man takes 6 hours 15 minutes in walking a distance and riding back to starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride back both ways is:

Options

A. 4 hours
B. 4 hours 30 minutes
C. 4 hours 45 minutes
D. 5 hours

Answer

To solve the problem step by step, we need to determine the time taken by the man to ride back both ways, given the time taken to walk and the time taken to walk and ride.

### Step 1: Convert the time into a single unit
First, we need to convert the time taken into hours and minutes for easier calculations.

- The total time taken for walking one way and riding back is **6 hours 15 minutes**.
- The total time taken for walking both ways is **7 hours 45 minutes**.

### Step 2: Convert hours and minutes to minutes
We convert both times to minutes:
- **6 hours 15 minutes** = \(6 \times 60 + 15 = 360 + 15 = 375\) minutes
- **7 hours 45 minutes** = \(7 \times 60 + 45 = 420 + 45 = 465\) minutes

### Step 3: Set up the equation
Let \(R\) be the time taken to ride one way, and \(W\) be the time taken to walk one way. We have the following equations based on the information provided:

1. \(W + R = 375\) (time taken for walking one way and riding back)
2. \(2W = 465\) (time taken for walking both ways)

### Step 4: Solve for \(W\)
From the second equation:
\[ 2W = 465 \]
\[ W = \frac{465}{2} = 232.5 \text{ minutes} \]

### Step 5: Substitute \(W\) back into the first equation
Now, substitute \(W\) back into the first equation to find \(R\):
\[ 232.5 + R = 375 \]
\[ R = 375 - 232.5 = 142.5 \text{ minutes} \]

### Step 6: Calculate the time taken to ride both ways
Since \(R\) is the time taken to ride one way, the time taken to ride both ways is:
\[ 2R = 2 \times 142.5 = 285 \text{ minutes} \]

### Step 7: Convert back to hours and minutes
Now, convert 285 minutes back to hours and minutes:
- \(285 \div 60 = 4\) hours and \(285 - 240 = 45\) minutes.

Thus, the time taken by him to ride back both ways is **4 hours 45 minutes**.

### Final Answer
The time taken by him to ride back both ways is **4 hours 45 minutes**.

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