Safety regulations require that the time between airplane takeoffs (on the same runway) will be at least 4 minutes. When taking off, the run time of an airplane on the runway is 24 seconds. Planes are on average waiting 5 minutes and 54 seconds for take-off. On average there are 12 planes taking off per hour. How many planes are either on the runway or waiting to take off?

1 plane either on the runway or waiting to take off

Step-by-step explanation:

We are given;

Frequency of take off = 12 planes per hour = 12/60 = 0.2 planes per minute

Waiting time on runway = 5 minutes 54 seconds = 5.9 minutes

Run time on runway = 24 seconds = 24/60 minutes = 0.4 minutes

To solve this question, we will use Little's law which is given by the formula;

System inventory = rate of flow × throughput time

Now, rate of flow is the same as Frequency of take off.

Thus, rate of flow = 0.2 planes per minute

Throughput time = Waiting time on runway + Run time on runway

Thus;

Throughput time = 5.9 minutes + 0.4 minutes

Throughput time = 6.3 minutes

Thus;

System inventory = 0.2 × 6.3 = 1.26 planes

Thus is approximately 1 plane.