In a 800 m race around a stadium having the circumference of 200 m, th

Because the track is 200m and the race is 800m, that means runners will go round the track 4 times.

Let speed of last runner be b so speed of first runner is 2b.

Since they meet in 5 mins. Last runner would have covered a distance of x and first runner 200+x.

For first runner,

200+x = 2b X 5

And distance covered by last runner

x = 5b


So

200 + 5b = 10b

5b = 200

b = 40.

So time taken for first runner to cover the track once.

t = 200/80

So time taken to complete the race

200/80 X 4

= 10 minutes.

Posted from my mobile device

Can anyone explain please how we are confidently saying that within 5 minutes the fast runner "must have" crossed one lap of 200m once? it can be twice or even thrice per see.

Thanks.
Bunuel

This is how I approached the question -

S of faster runner (Sf)= 2 * speed of slower runner (Ss)
=> Sf = 2 * Ss

Hence, when the faster runner has completed a lap, slower runner has completed half of the first lap.
When the faster runner has completed the second lap, the slower runner is completing the first lap..
This duration is given as 5 mins.. So if the faster runner takes 5 mins to complete 2 laps, he/she takes 10 mins to complete 4 laps..

If you do not consider that t = 5 mins for the first time the two runners meet, then the two runners will meet after faster runner has completed 4 laps and the slower one has completed 2 laps.. In this case the faster runner takes 5 mins to complete 4 laps hence takes 5 + 5/4 mins to complete 5 laps.. This isn't an option (also, per what I have noticed, the time mentioned in these questions is generally for the first meet unless specially mentioned.. in this case you can see that 5+ 5/4 isn't an option..)

I think the speed of the fastest runner would be 80, ie, 2s: As a result, answer should be 10 mins