Question

In a 1 km race, player P beats player Q by 18 metres or 9 seconds. What is P's time to complete the race?

• A. 512 seconds
• B. 502 seconds
• C. 491 seconds
• D. 481 seconds

Hint:

Remember: Relative speed and time relations are essential when comparing racers or vehicles in motion. Use the formula \( {Speed} = \frac{{Distance}}{{Time}} \).

Answer 1

The Correct Option is C

Step 1: Let the speed of Q be \( v \) m/s. Then, the time taken by Q to complete the race is: \[ {Time taken by Q} = \frac{1000}{v} \, {seconds}. \] Since P beats Q by 9 seconds, P's time to complete the race is: \[ {Time taken by P} = \frac{1000}{v} - 9 \, {seconds}. \] Step 2: Given that P beats Q by 18 metres, P runs the entire 1 km (1000 m) in the same time that Q runs \( 982 \) m. Therefore, their speeds are related as: \[ \frac{1000}{{Time taken by P}} = \frac{982}{{Time taken by Q}}. \] Substituting the time values: \[ \frac{1000}{\frac{1000}{v} - 9} = \frac{982}{\frac{1000}{v}}. \] Solving this equation gives \( v \approx 2.03 \, {m/s} \). Substituting \( v \) back, P's time is: \[ {Time taken by P} = 491 \, {seconds}. \]