A runs 3 times as fast as B. If A gives B a start of 30 meters, how far must the goal on the race course be so that A and B reach it at the same time?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 45 m
Let the goal be d metres from the start and let B’s speed be v, so A’s speed is 3v. With the start of 30 m, B runs only \(d - 30\) metres. They reach the goal at the same time:
\( \displaystyle \frac{d}{3v} = \frac{d - 30}{v} \)
\(d = 3(d - 30)\)
\(2d = 90\)
\(d = 45\) m
Check: A runs 45 m while B runs 15 m, one third of the distance.