[Guest]

Jack dances clockwise around the Maypole, making one revolution every five seconds. starting from a point diametrically opposite Jack's starting point, Jill dances anticlockwise, making one revolution every six seconds.

How many times do they pass each other in a minute?

[HoustonHokie]

they first meet after 1.36 seconds, and then they meet every 2.72 seconds after that. So, at the end of 60 seconds, they will have met 22 times and end up in the same positions they started in.

[Guest]

yes, well done

[Guest]

I have the same answer for 60 seconds, but a different one for their first meeting.

They meet after 1.375 seconds and every 2.75 seconds after that. This still makes them pass each other 22 times in 60 seconds.

[Guest]

Jack dances clockwise around the Maypole, making one revolution every five seconds. starting from a point diametrically opposite Jack's starting point, Jill dances anticlockwise, making one revolution every six seconds.

How many times do they pass each other in a minute?

I think you guys are off, this is the correct answer:

Since they are going opposite directions and at a rate that puts them at the starting point at 60s it's simple. Add the revolutions that each one makes, so 12 plus 10, so 22. EXCEPT the question says "pass" not "meet", so don't count the last one.

The answer is they pass 21 times.

[Guest]

Simple yet effective use of a little Logic...

First off assumptions:

-Each person will pass each other person going the opposite direction once during each revolution

Now the workings out:

Jack will make 12 (60/5) revolutions in total

Jill will make 10 (60/6) revolutions in total

With the assumptions made earlier that would mean they make a total of 22 passes within the allotted time.

If they had started at the same point, whey would of met each other 22 times, but only passed each other 21 times.

[Guest]

They will pass each other at t=1.3636 seconds and every 2.727 seconds thereafter, for a total of 22 times in 60 seconds. They will cross at Jack's position at t=15 and t=45 seconds. Their points of intersection inscribe two identical 11 pointed stars with the vertices 32.727 degrees apart (though each consecutive intersection is 163.636 degrees apart) If Jill travels in a circle 6/5 the radius of Jack's, they can travel at the same speed.

[Guest]

Jack dances clockwise around the Maypole, making one revolution every five seconds. starting from a point diametrically opposite Jack's starting point, Jill dances anticlockwise, making one revolution every six seconds.

How many times do they pass each other in a minute?

I always feel I am missing something as soon as math is involved, but

60/5 = 12

60/6 = 10

As the one doesn't "lap" the other, they can each only pass the other once per revolution.

So 12 + 10 = 22

[Guest]

I always feel I am missing something as soon as math is involved, but

60/5 = 12

60/6 = 10

As the one doesn't "lap" the other, they can each only pass the other once per revolution.

So 12 + 10 = 22

Yes, except the last one doesn't count because they don't pass. They end up at the same spot. So one less than your answer is correct.

[Guest]

Yes, except the last one doesn't count because they don't pass. They end up at the same spot. So one less than your answer is correct.

They don't end up in the same spot as each other, they each end up in the same spot in which they began - diametrically opposite each other.

[Guest]

They don't end up in the same spot as each other, they each end up in the same spot in which they began - diametrically opposite each other.

Ah, yes, a careful re-reading of the question indicates you are absolutely right!