Monica takes 9hrs 15 minutes in walking a distance and riding back to same place where she started. She could walk both ways in 11 hrs 12 minutes. The time taken by her t ride back both ways is :
A. 7 hrs 18 min
B. 7 hrs 35 min
C. 7 hrs 45 min
D. 7 hrs 15 min

Options

A. B
B. A
C. D
D. C

Answer

To solve the problem step by step, we will first convert the given times into a consistent format (preferably minutes) and then set up equations based on the information provided.

### Step 1: Convert the times into minutes
- Monica takes **9 hours 15 minutes** to walk one way and ride back, which can be converted to minutes:
\[ 9 \text{ hours} = 9 \times 60 = 540 \text{ minutes} \]
\[ 9 \text{ hours 15 minutes} = 540 + 15 = 555 \text{ minutes} \]

- She takes **11 hours 12 minutes** to walk both ways, which can also be converted to minutes:
\[ 11 \text{ hours} = 11 \times 60 = 660 \text{ minutes} \]
\[ 11 \text{ hours 12 minutes} = 660 + 12 = 672 \text{ minutes} \]

### Step 2: Set up the equations
Let:
- \( x \) = time taken to walk one way (in minutes)
- \( y \) = time taken to ride one way (in minutes)

From the information given:
1. The total time for walking one way and riding back is:
\[ x + y = 555 \quad \text{(Equation 1)} \]
2. The total time for walking both ways is:
\[ 2x = 672 \quad \text{(Equation 2)} \]

### Step 3: Solve Equation 2 for \( x \)
From Equation 2:
\[ 2x = 672 \implies x = \frac{672}{2} = 336 \text{ minutes} \]

### Step 4: Substitute \( x \) back into Equation 1
Now, substitute \( x \) into Equation 1:
\[ 336 + y = 555 \]
Solving for \( y \):
\[ y = 555 - 336 = 219 \text{ minutes} \]

### Step 5: Calculate the total time taken to ride both ways
Since \( y \) is the time taken to ride one way, the total time taken to ride both ways is:
\[ 2y = 2 \times 219 = 438 \text{ minutes} \]

### Step 6: Convert the total riding time back to hours and minutes
To convert 438 minutes back to hours and minutes:
\[ 438 \div 60 = 7 \text{ hours} \quad \text{(with a remainder of 18 minutes)} \]
Thus, the total riding time is:
\[ 7 \text{ hours } 18 \text{ minutes} \]

### Final Answer
The time taken by Monica to ride back both ways is **7 hours 18 minutes**.