60 trucks arrive at a paving plant every morning as shown by the curve labeled A

Question

60 trucks arrive at a paving plant every morning as shown by the curve labeled A (t) in Figure 1 below, which represents cumulative arrivals as a function of time of day. the plant begins operation at 8:00 Am and can fill a truck every 4 minutes. After a truck is filled, it immediately leaves the plant. the trucks are filled on a first come, first served basis. At what time does the 60^th truck leave the plant? What is the longest time any truck spends in the paving plant? the parking area at the plant must be large enough to hold at least how many trucks?

Explanation / Answer

(a) Here j = A(t) gives the cumulative number

Now A-1(j) = t represents the inverse function and thus the time t at which the jth truck arrives

Now A-1(60) = 11:30 AM
Now that means 60th truck arrives at 11:30 AM

As the plant needs 4 minutes to fill the truck and so after 4 minutes it leaves the plane

Hence The truck leaves the plant at 11:34 AM

(b) As the first few trucks arrive before 8:00 AM and the operation starts at 8:00 AM

The truck starts from 7:30

Hence the longest time they spent in a planet is 30minutes + 4minutes = 34 minutes

(c) Since A(t) = 20 before 8:00 AM

This means that there should be space of atleast 20 trucks in the parking area

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.