Conveyor Merge Timing

Scenario

A conveyor merge has two infeeds (Left, Right) feeding one takeaway

. Sensors show:

• Left produces a carton every 20 seconds
• Right produces a carton every 30 seconds

Both start at the same moment.

At what times will cartons arrive simultaneouslyat the merge?

Answer and Explanation

60 Seconds

Think of each conveyor as running on its own “rhythm.”

• The Left infeed drops a carton every 20 seconds → 20, 40, 60, 80, 100, …
• The Right infeed drops a carton every 30 seconds → 30, 60, 90, 120, …

What we’re really asking is: when do those two rhythms line up again?

If you list out the arrival times, the first time you see the same number on both lists is 60 seconds. That’s the first moment when both conveyors deliver a carton at exactly the same time.

From there, the pattern just repeats. Every 60 seconds, both sides complete a whole number of cycles:

• Left has delivered 3 cartons (3 × 20 s)
• Right has delivered 2 cartons (2 × 30 s)

So the merge sees simultaneous arrivals at: 1:00, 2:00, 3:00, 4:00, …

In engineering terms, 60 seconds is simply the least common multiple of the two cycle times—the shortest interval where both processes sync back up.