All South Carolina bound passengers at the Detroit Metro Air

All South Carolina bound passengers at the Detroit Metro Airport check in and are directed to the main security gate (checkpoint #1). About 10% of the passengers who are directed to checkpoint #1 DO NOT get in line. Rather they proceed to an alternate checkpoint for security clearance. If the average line at checkpoint #1 has 100 people in it and if on average, 650 per hour arrive at checkpoint #1, then how long (in minutes) do those staying at checkpoint #1 wait in line?

Answers:

a. 10.26 minutes

b. 8.39 minutes

c. 5.13 minutes

d. 9.23 minutes

Solution

Average people at Checkpoint #1 in hour = 650

As 10% of the passengers who are directed to checkpoint #1 DO NOT get in line, therefore in hour total people at checkpoint # 1 will be 585.

Therefore, in a minute avg people at checkpoint #1 will be 585/60 = 9.75.

Average Line at checkpoint #1 has 100 people

Hence wait in minutes at Checkpoint #1 will be 100/9.75 = 10.256 minutes

Answer : 10.26 minutes

I/R =T

I = 100

R = 9.75/minute

T = 100/9.75 = 10.26 minutes