tease me

[razorback]

2 cyclists go round a track one completes 16 circuits per hour the other 10 circuits per hour.if they both simultaneously start from the same point how long will it be before they are next exactly together

[gen2]

Shouldn't this be in the Riddles section?

Ten minutes

[wildwood]

2 min. 20.625 seconds.

[Rtaxron]

You ask at this time of the night, give us a break, I am on my 2nd bottle of wine, slurp.

[MatydaLover]

After 1 hour, the slower will have completed 10 laps, the faster 16. So the faster catches the slower 6 times each hour ... or once every one-sixth of an hour.

i.e. After one-sixth of an hour (10 mins), the slower has done one-and-four-sixths laps, the faster has done two-and-four-sixths laps ... they have met again four-sixths of a lap. After 20 mins they meet again a further four-sixths of a lap from there.

Counting the laps might make them sleepy, though.

[MatydaLover]

My apologies to gen2. I scanned the answers too quickly and thought everyone was late-nighting. Inexcusable, but unintenional.

[Tom Braider]

This is a trick question, isn't it? If the cyclists set off in opposite directions they'd be together again after 4.875 minutes.

[MatydaLover]

If they went in opposite directions, their displacement would be the same as if one remained at the start and the other sped off at 26 lph. Thus they'd meet again in 60/26 or 2 and 8/26 minutes. About 2' 18.46" ... very close to wildwood's answer.

[wildwood]

Oh Matyda... mine was just flippant answers. lol

The question can not be answered as razorback wants an exact answer which requires variables. 10 minutes would be correct if the Q is taken at face value but I suspect there are ambiguous additives like The first lap will take longer than the second due to the rate of acceleration at the start or the circuit is on a hill side which would effect the lapping times.