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In this problem, we are given that:

- P beats Q by 120 meters or 30 seconds in a 1 km (1000 meters) race.
- We need to find the time taken by P to cover the entire 1 km race.

Let's assume the time taken by P to cover the race is \( t_P \) seconds.

### Step-by-Step Solution:

1. Let the speed of P be \( v_P \) meters per second.
   \[
   v_P = \frac{1000}{t_P}
   \]
   
2. P beats Q by 120 meters or 30 seconds. This means that when P finishes the 1000 meters, Q is 120 meters behind, or equivalently, Q takes 30 more seconds to finish the race.
   
3. The total distance for the race is 1000 meters, and Q would cover the remaining 120 meters in 30 seconds. So, Q's speed \( v_Q \) is:
   \[
   v_Q = \frac{120}{30} = 4 \text{ m/s}
   \]
   
4. Using Q's speed, we know that Q would take \( t_Q \) seconds to finish the full 1000 meters:
   \[
   t_Q = \frac{1000}{v_Q} = \frac{1000}{4} = 250 \text{ seconds}
   \]
   
5. Since P beats Q by 30 seconds, the time taken by P to complete the race is:
   \[
   t_P = t_Q - 30 = 250 - 30 = 220 \text{ seconds}
   \]

### Answer:
The time taken by P to cover the 1 km race is 220 seconds.

Would you like further details or clarification on any step? Here are some related questions to explore:

1. How can we calculate the speed of Q in this problem?
2. What would happen if P and Q were closer in their speeds?
3. How would the solution change if the distance of the race were different?
4. Can you derive a formula for the time difference between P and Q for any race distance?
5. What other methods could be used to solve this type of problem?

**Tip:** Always keep units consistent when solving problems involving time, distance, and speed!

In 1 km linear race, P beats Q by 120 metres or 30 sec. What is the time taken by P to cover the race?

Learn how to calculate the time taken by P to cover a 1 km race when P beats Q by 120 meters or 30 seconds. This problem explores concepts of speed, distance, and relative time, making it ideal for students in Grades 8-10.

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