math riddle need help w/ answer and getting correct equation

[ccandykk]

You and a friend are swimming laps in a pool. You swim one lap every four minutes, your friend swims one lap every five minutes. If you start at the same time from the send of the pool, in how many minutes will both of you be at the starting point again? How many times will you have passed each other prior to that time?

I believe that 40 minutes is the answer to the first question, if I'm wrong please let me know. I need help It has been 15 years since I have been in school and it is like starting over.

 

[Loren]

How did you arrive at 40? Granted...40 is a multiple of 4 and also a multiple of 5. Are there other numbers that are multiples of both 4 and 5 that you might want to consider?

 

[ccandykk]

In 20 minutes you are both at the opposite ends of the pool, I really did it the primitive way lines on paper and labeled them appropriate increments, It is the times passing each other I am stumped on

 

[Loren]

I guess it hinges on your definition of the word "lap". I'm thinking that a lap is one circuit, which, to me, means up and back to the starting point. If you define a lap as just going from one end to the other, then you are correct. I would be interested in what you come up with.