P covers 1 km in 4 min 40 s ,while Q covers the same distance in 5 mint .By what distance does P defeat Q?

Answer

To solve the problem of how much distance P defeats Q by, we will follow these steps:

### Step 1: Convert P's time to seconds
P covers 1 km in 4 minutes and 40 seconds.
- Convert 4 minutes to seconds:
\[ 4 \text{ minutes} = 4 \times 60 = 240 \text{ seconds} \]
- Add the remaining 40 seconds:
\[ \text{Total time for P} = 240 + 40 = 280 \text{ seconds} \]

### Step 2: Convert Q's time to seconds
Q covers the same distance in 5 minutes.
- Convert 5 minutes to seconds:
\[ 5 \text{ minutes} = 5 \times 60 = 300 \text{ seconds} \]

### Step 3: Calculate the speed of P and Q
- Speed of P:
\[ \text{Speed of P} = \frac{1 \text{ km}}{280 \text{ seconds}} = \frac{1000 \text{ meters}}{280 \text{ seconds}} \approx 3.57 \text{ m/s} \]
- Speed of Q:
\[ \text{Speed of Q} = \frac{1 \text{ km}}{300 \text{ seconds}} = \frac{1000 \text{ meters}}{300 \text{ seconds}} \approx 3.33 \text{ m/s} \]

### Step 4: Determine the time taken by Q to cover the distance P takes
Now we need to find out how far Q has traveled when P finishes 1 km (280 seconds).
- Distance covered by Q in 280 seconds:
\[ \text{Distance} = \text{Speed of Q} \times \text{Time} = 3.33 \text{ m/s} \times 280 \text{ seconds} \approx 933.33 \text{ meters} \]

### Step 5: Calculate the distance by which P defeats Q
- The distance by which P defeats Q is the difference between the distance covered by P and the distance covered by Q:
\[ \text{Distance defeated} = 1000 \text{ meters} - 933.33 \text{ meters} \approx 66.67 \text{ meters} \]

### Final Answer
P defeats Q by approximately **66.67 meters**.

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