Ram travels a certain distance at 3km/hr and reaches 15 min late if he travels at 4 km/hr he reaches 15 min earlier the distance he has to travel is

Options

A. 4.5km
B. 6km
C. 7.2km
D. 12km

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
Ram travels a certain distance at two different speeds: 3 km/hr and 4 km/hr. We know that at 3 km/hr, he is 15 minutes late, and at 4 km/hr, he is 15 minutes early. The total time difference between the two scenarios is 30 minutes.

### Step 2: Convert Time Difference to Hours
Since the time difference is given in minutes, we convert it to hours for easier calculations:
- 30 minutes = 30/60 hours = 0.5 hours.

### Step 3: Use the Formula for Distance
We can use the formula for distance based on the speeds and the time difference:
\[ \text{Distance} = \frac{s_1 \times s_2}{s_2 - s_1} \times \text{Time Gap} \]
Where:
- \(s_1 = 3 \text{ km/hr}\) (slower speed)
- \(s_2 = 4 \text{ km/hr}\) (faster speed)
- Time Gap = 0.5 hours

### Step 4: Substitute the Values into the Formula
Now, we substitute the values into the formula:
\[ \text{Distance} = \frac{3 \times 4}{4 - 3} \times 0.5 \]

### Step 5: Calculate the Distance
Now we calculate the values step by step:
1. Calculate \(3 \times 4 = 12\).
2. Calculate \(4 - 3 = 1\).
3. Now substitute these values back into the formula:
\[ \text{Distance} = \frac{12}{1} \times 0.5 = 12 \times 0.5 = 6 \text{ km} \]

### Step 6: Conclusion
The distance Ram has to travel is 6 km.