Question

A manager observes that on average, 5 students per minute enter the campus cafeteria. 10% of the students that enter the cafeteria see a long line and leave without entering the line. Given students are leaving before entering the process, the manager must determine the rate at which students are entering the process. On average, 18 students are waiting in line and we can assume that any student that enters the line will not leave.
1) I = _______

2) R = _______

3) On average how long does a student spend in the cafeteria line? Time measurement must be in minutes.

Answer 1

Answer:

1. The rate, at which the students are entering the process is 4.5 students per minute.

2. On average a student spends 4 minutes on the cafeteria line.

Explanation:

1. 5 students enters the cafeteria per minutes.

10% of students does not enter the line.

therefore, percentage of students entering the line will be 100-10 = 90%.

The rate at which students enters the line will be 90% of overall students entering the cafeteria per minute:

$\frac{90}{100}$ × 5 ($\frac{students}{minute}$

= 4.5  $\frac{students}{minute}$

2. The average time spend by a student on the line will be:

the time rate of a student entering the line, which is the inverse of the rate of students entering the line : $\frac{1}{4.5}$ × the number of students waiting on the line, which is 18.

⇒ $\frac{1}{4.5}$ × 18 = 4 minutes.