A runs 9 times slower than B. If B gives A a start of 80 meters, how far must be the winning post on the tracks so that A and B reach there at the same time?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 90 meters
“A runs 9 times slower than B” means that B’s speed is 9 times A’s speed. Let A’s speed be v m/s, so B’s speed is 9v m/s.
Let the winning post be D metres from B’s starting point. With a start of 80 m, A has to run only D − 80 metres.
They reach the post together, so their times are equal:
\( \displaystyle \frac{D - 80}{v} = \frac{D}{9v} \)
\(9(D - 80) = D\)
\(9D - 720 = D\)
\(8D = 720\)
\(D = 90\)
So the winning post must be 90 metres away. Check: B runs 90 m while A runs 10 m, and \(90 = 9 \times 10\).