In 1 km race,P beats Q by 72 m in 12 s. Find the P s time over the course.

Options

A. 155-s
B. 151 s
C. 154-s
D. 160 s

Answer

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

### Step 1: Understand the given information
P beats Q by 72 meters in a 1 km race (1000 meters) in 12 seconds. This means when P finishes the race, Q has only covered 1000 - 72 = 928 meters.

### Step 2: Calculate Q's speed
To find Q's speed, we can use the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Q covers 928 meters in 12 seconds.
\[ \text{Speed of Q} = \frac{928 \text{ m}}{12 \text{ s}} \]

### Step 3: Calculate Q's speed in meters per second
Calculating the speed:
\[ \text{Speed of Q} = \frac{928}{12} = 77.33 \text{ m/s} \]

### Step 4: Calculate the time taken by Q to complete the 1 km race
Now, we need to find out how long it would take Q to cover the full 1000 meters.
Using the speed we calculated:
\[ \text{Time taken by Q} = \frac{1000 \text{ m}}{\text{Speed of Q}} = \frac{1000}{77.33} \]

### Step 5: Perform the calculation
Calculating the time:
\[ \text{Time taken by Q} = \frac{1000}{77.33} \approx 12.92 \text{ seconds} \]

### Step 6: Calculate P's time
Since P beats Q by 72 meters, we know that P takes 12 seconds less than Q to finish the race. Therefore, we can find P's time:
\[ \text{Time taken by P} = \text{Time taken by Q} - \text{Time difference} \]
\[ \text{Time taken by P} = 12.92 - 12 \approx 0.92 \text{ seconds} \]

### Step 7: Finalize P's time
Thus, P's time over the course is approximately:
\[ \text{Time taken by P} \approx 12.92 \text{ seconds} \]

### Summary of the solution
P's time over the course is approximately 12.92 seconds.

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