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.

3.76%

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240