P can run a kilometre in 4 minutes 50 seconds and Q in 5 minutes. By what distance can P beat Q ?

Options

A. 30 m
B. `(16) 2/3` m
C. `(33) 1/3` m
D. `(26) 2/3` m

Answer

To solve the problem of how far P can beat Q, we will follow these steps:

### Step 1: Convert P's time to seconds
P can run 1 kilometer in 4 minutes and 50 seconds.
- Convert 4 minutes to seconds:
\[ 4 \text{ minutes} = 4 \times 60 = 240 \text{ seconds} \]
- Add the remaining 50 seconds:
\[ 240 + 50 = 290 \text{ seconds} \]
Thus, P takes 290 seconds to run 1 kilometer.

### Step 2: Convert Q's time to seconds
Q can run 1 kilometer in 5 minutes.
- Convert 5 minutes to seconds:
\[ 5 \text{ minutes} = 5 \times 60 = 300 \text{ seconds} \]
So, Q takes 300 seconds to run 1 kilometer.

### Step 3: Calculate the time difference
Now, we find the difference in time taken by P and Q:
\[ \text{Time difference} = 300 \text{ seconds} - 290 \text{ seconds} = 10 \text{ seconds} \]

### Step 4: Calculate the distance Q covers in the time difference
Next, we need to determine how far Q can run in the 10 seconds that P finishes before Q.
- Q's speed can be calculated as:
\[ \text{Speed of Q} = \frac{1000 \text{ meters}}{300 \text{ seconds}} = \frac{10}{3} \text{ meters/second} \]
- Now, calculate the distance Q covers in 10 seconds:
\[ \text{Distance covered by Q in 10 seconds} = \text{Speed} \times \text{Time} = \frac{10}{3} \times 10 = \frac{100}{3} \text{ meters} \]

### Step 5: Conclusion
Thus, P beats Q by the distance of:
\[ \frac{100}{3} \text{ meters} \approx 33.33 \text{ meters} \]

### Final Answer
P can beat Q by approximately 33.33 meters.

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