Josna takes 4 hrs 30 minutes in walking a distance and riding back to same place where she started. She could walk both ways in 5 hr. 40 minutes. The time taken by her to ride back both ways is

Options

A. 3 hr. 20 min
B. 3 hr. 35 min
C. 3 hr. 45 min
D. 3 hr. 15 min

Answer

To solve the problem step by step, we can break it down as follows:

### Step 1: Convert the time into hours and minutes
We know that:
- Josna takes **4 hours 30 minutes** for walking one way and riding back.
- She takes **5 hours 40 minutes** for walking both ways.

### Step 2: Calculate the time taken for one way walking
To find the time taken for walking one way, we divide the total walking time by 2:
- Total walking time for both ways = 5 hours 40 minutes
- Convert 5 hours 40 minutes into minutes:
\[ 5 \times 60 + 40 = 300 + 40 = 340 \text{ minutes} \]
- Now, divide by 2:
\[ \frac{340}{2} = 170 \text{ minutes} \]
- Convert back to hours and minutes:
\[ 170 \text{ minutes} = 2 \text{ hours and } 50 \text{ minutes} \]

### Step 3: Calculate the time taken for one way riding
Now, we know the time taken for one way walking is **2 hours 50 minutes**. We can find the time taken for one way riding by subtracting the walking time from the total time taken for one way (walking + riding):
- Total time for one way (walking + riding) = 4 hours 30 minutes
- Convert 4 hours 30 minutes into minutes:
\[ 4 \times 60 + 30 = 240 + 30 = 270 \text{ minutes} \]
- Now, subtract the walking time (2 hours 50 minutes) from this:
- Convert 2 hours 50 minutes into minutes:
\[ 2 \times 60 + 50 = 120 + 50 = 170 \text{ minutes} \]
- Now subtract:
\[ 270 - 170 = 100 \text{ minutes} \]
- Convert back to hours and minutes:
\[ 100 \text{ minutes} = 1 \text{ hour and } 40 \text{ minutes} \]

### Step 4: Calculate the time taken for two way riding
Now that we have the time for one way riding, we can find the total time for riding both ways:
- Time for one way riding = 1 hour 40 minutes
- Convert 1 hour 40 minutes into minutes:
\[ 1 \times 60 + 40 = 60 + 40 = 100 \text{ minutes} \]
- For both ways, multiply by 2:
\[ 2 \times 100 = 200 \text{ minutes} \]
- Convert back to hours and minutes:
\[ 200 \text{ minutes} = 3 \text{ hours and } 20 \text{ minutes} \]

### Final Answer
The time taken by Josna to ride back both ways is **3 hours 20 minutes**.

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