Question

At a taxi stand, there is usually a line of taxicabs waiting to pickup passengers. The number of taxicabs there varies in time, but eventually, they all leave with a passenger. On average, there are 6 cars at the taxi stand. A car arrives at the taxi stand to join the line every 5 minutes on average. What is the average time a taxi driver has to wait until s/he departs with a customer? Provide your answer in minutes.

Answer 1

The average waiting time for a taxi driver at the stand is 30 minutes, calculated based on the average of 1 taxi arriving every 5 minutes and 6 taxis being present on average at the stand.

Step-by-step explanation:

To calculate the average waiting time for a taxi driver at the taxi stand, we can use the information provided. If there are on average 6 cars at the taxi stand and a car arrives to join the line every 5 minutes, we infer that the arrival rate of taxis is 1 taxi per 5 minutes.

Since there are 6 taxis on average, and each taxi will leave with the next arriving customer, each taxi effectively has to wait for 6 customer arrivals to be at the front of the line and depart with a passenger. If one customer arrives every 5 minutes on average, then 6 customers will take 30 minutes to arrive (5 minutes x 6).

Therefore, the average time a taxi driver has to wait until he or she departs with a customer is 30 minutes.