Question: Computing Messages per Second

I'm trying to rationalize this in my head, any help is welcome.

"1 million individuals, each participate in 3 text message conversations per hour.

Each text message conversation involves 6 text messages over a 300 second (5 minute) period.

You are designing a system to handle this load. What is the number of text messages per second being generated, why?"

Here's my reckoning

    1 million x 3 text conversations/hour x 1/3600 x 6 messages per second

But, that doesn't reflect the fact that each exchange lasts 5 minutes and therefore each text conversation only produces 1 text message per minute.