Question

Boxes of bad vampire novels arrive, on average, every 8 minutes at an industrial-strength shredder. The standard process to load, shred, and unload each shredded boxload takes 6.5 minutes. What is the average time from when a box of novels arrives until shredding is complete (in hours)?

Answer 1

Answer:

0.578 hours

Step-by-step explanation:

If boxes of books arrive at a rate of 1 per 8 minutes, the number of boxes per hour is:

$\mu =\frac{1}{8}*60=7.5/hour$

If the service rate is 1 box per 6.5 minutes, the number of boxes per hour is:

$\mu =\frac{1}{6.5}*60=9.231/hour$

The average time from when a box of novels arrives until shredding is complete is:

$t=\frac{1}{\mu-\lambda}=\frac{1}{9.231-7.5} \\t=0.578\ hours$

The average time in the system is 0.578 hours.