After how many seconds are both runners next…

After how many seconds are both runners next at the starting point together?

Question 73

HardOriginal question

A and B run round a 400 m circular track from the same point at the same moment, A at 5 m/s and B at 3 m/s.

After how many seconds are both runners next at the starting point together?

200 secondsCorrect answerYour answer240 secondsCorrect answerYour answer400 secondsCorrect answerYour answer1,200 secondsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

A laps in $\frac{400}{5} = 80$ s and B in $\frac{400}{3}$ s; both are back at multiples of these.
In thirds of a second: $\text{LCM}(240, 400) = 1{,}200$ , so 400 seconds (A 5 laps, B 3 laps).

Worth noting

200 seconds is their first meeting anywhere on the track, not at the start.

Ten questions from Races & Games, at your own pace.

Ten questions from Races & Games, at your own pace.