A person X started 3 hours earlier at 40 km/h from a place P then another person Y followed him at 60 km/h started his journey at 3 o'clock afternoon.what is the distance travelled by Y to overtake X?

Options

A. 180 km
B. 420 km
C. 320 km
D. 360 km

Answer

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

### Step 1: Calculate the distance traveled by X in 3 hours
- **Speed of X** = 40 km/h
- **Time traveled by X** = 3 hours

Using the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

So, the distance traveled by X in 3 hours is:
\[ \text{Distance} = 40 \, \text{km/h} \times 3 \, \text{hours} = 120 \, \text{km} \]

### Step 2: Determine the relative speed between Y and X
- **Speed of Y** = 60 km/h
- **Speed of X** = 40 km/h

Since both are moving in the same direction, the relative speed is:
\[ \text{Relative Speed} = \text{Speed of Y} - \text{Speed of X} = 60 \, \text{km/h} - 40 \, \text{km/h} = 20 \, \text{km/h} \]

### Step 3: Calculate the time taken by Y to overtake X
- The distance between Y (who starts at 3 PM) and X (who is already 120 km ahead) is 120 km.

Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]

So, the time taken for Y to overtake X is:
\[ \text{Time} = \frac{120 \, \text{km}}{20 \, \text{km/h}} = 6 \, \text{hours} \]

### Step 4: Calculate the distance traveled by Y to overtake X
Now, we can find the distance Y travels in the time it takes to overtake X:
- **Speed of Y** = 60 km/h
- **Time taken to overtake** = 6 hours

Using the distance formula again:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

So, the distance traveled by Y is:
\[ \text{Distance} = 60 \, \text{km/h} \times 6 \, \text{hours} = 360 \, \text{km} \]

### Final Answer
The distance traveled by Y to overtake X is **360 km**.

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