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. The time taken by Q to complete the 1000 m race is \( \frac{1000}{v} \) seconds. Since P beats Q by 9 seconds, P's time is \( \frac{1000}{v} - 9 \) seconds. Step 2: P beats Q by 18 metres, meaning P completes 1000 m in the same time Q completes \( 1000 - 18 = 982 \) m. Their speeds are related by the ratio of distances covered in equal time: \( \frac{1000}{\text{Time taken by P}} = \frac{982}{\text{Time taken by Q}} \). Substituting the time expressions: \( \frac{1000}{\frac{1000}{v} - 9} = \frac{982}{\frac{1000}{v}} \). Solving this equation yields \( v \approx 2.03 \) m/s. Substituting this value back, P's time to complete the race is \( \frac{1000}{2.03} - 9 \approx 491 \) seconds.