In a 720 m race, A runs at 8 m/s and B runs at 6 m/s. A gives B a start of 180 m. Which of the following statements are correct?
(A) A takes 90 seconds to finish the race.
(B) B takes 120 seconds to reach the finishing line.
(C) The race ends in a dead heat.
(D) Without any start, A would beat B by 180 m.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (C) and (D) only
With a start of 180 m, B has to run only \(720 - 180 = 540\) m. The time = distance ÷ speed for each runner is:
\(\text{Time of A} = 720 \div 8 = 90 \text{ s}\)
\(\text{Time of B} = 540 \div 6 = 90 \text{ s}\)
\(\text{Distance run by B in 90 s} = 6 \times 90 = 540 \text{ m}\)
So both runners finish after 90 seconds, and in A’s 90 seconds B covers only 540 m.
Checking the statements
(A) A takes 90 seconds to finish the race. — Correct. \(720 \div 8 = 90\) seconds.
(B) B takes 120 seconds to reach the finishing line. — Incorrect. B runs only 540 m, which takes \(540 \div 6 = 90\) seconds; 120 seconds would be for the full 720 m.
(C) The race ends in a dead heat. — Correct. Both finish at 90 seconds.
(D) Without any start, A would beat B by 180 m. — Correct. When A finishes 720 m in 90 seconds, B has run \(6 \times 90 = 540\) m.