Jessie manages a call center. There are two types of callers: new callers and members. Phone calls from new callers arrive at a rate of 15 callers per hour, while calls from members arrive at a rate of 10 callers per hour. For each caller type, the inter-arrival times are exponentially distributed.

Currently, there are two waiting lines: one waiting line for new callers and a different line for members. Each line has one dedicated staff member to provide service to callers in that line, and the staff member only provides service to their assigned line. Each staff member has the same average service rate of 20 callers per hour, and the service times are exponentially distributed.

Question

Suppose Jessie merges the two waiting lines into one line, that is, the two caller types are all asked to wait in a single waiting line.

What is the average arrival rate to this new multi-server queue? (Answer in callers per hour)