In a 600 m race, A runs at 36 km/h and B runs at 30 km/h. By how many metres does A beat B?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 100 m
The race is in metres, so the speeds are changed to metres per second (multiply by \(\frac{5}{18}\)).
\(\displaystyle 36 \text{ km/h} = 36 \times \frac{5}{18} = 10 \text{ m/s}\)
\(\displaystyle 30 \text{ km/h} = 30 \times \frac{5}{18} = \frac{25}{3} \text{ m/s}\)
\(\text{Time taken by A} = 600 \div 10 = 60 \text{ s}\)
\(\displaystyle \text{Distance run by B in 60 s} = 60 \times \frac{25}{3} = 500 \text{ m}\)
When A finishes, B is still \(600 - 500 = 100\) m behind. So A beats B by 100 m.
Why the other options are incorrect
Option (1) 12 m — Incorrect. B takes 72 s, so A wins by 12 seconds; 12 is the lead in time, not in metres.
Option (2) 120 m — Incorrect. This is \(600 \times \frac{6}{30}\), which compares the speeds with B’s speed; B covers \(\frac{5}{6}\) of A’s distance, so the gap is \(\frac{1}{6}\) of 600 m.
Option (4) 60 m — Incorrect. In the 60 s that A takes, B runs 500 m, so the gap is 100 m, not 60 m.