Currently, you see 10 gates going in the East Entrance. On average, gate agents take 35 seconds to process a customer through the gate by scanning a QR Code. This processing time is exponentially distributed. Each gate has one gate agent, and each agent has his/her own line. You estimate that, on average, 50 fans arrive to the East Entrance (all 10 gates) every 3 minutes.

The arrivals are exponentially distributed. How many fans, on average, are waiting to be serviced at one gate?

how did they get 34.03 fans?