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A conveyor belt is used to send burgers through a grilling machine. If the grilling machine is 1.2 m long and the burgers require 2.8 min to cook, how fast must the conveyor belt travel? If the burgers are spaced 25 cm apart, what is the rate of burger production (in burgers/min)?

Short Answer

Expert verified
The conveyor belt must travel at approximately 0.4286 m/min, producing about 1.71 burgers per minute.

Step by step solution

01

Understand the Problem

The machine is 1.2 meters long, and it takes the burgers 2.8 minutes to pass through. We need to find the speed of the conveyor belt in meters per minute first and then find out how many burgers can be produced per minute.
02

Calculate Conveyor Belt Speed

The speed of the conveyor belt is calculated by dividing the length of the grilling machine by the cooking time required. So the speed is given by: \[ \text{Speed} = \frac{1.2 \text{ m}}{2.8 \text{ min}} \approx 0.4286 \text{ m/min} \]
03

Understand Burger Spacing and Production

Burgers are spaced 25 cm apart on the conveyor, which can be converted to meters (0.25 m). This indicates that a new burger begins processing every time the conveyor moves 0.25 meters.
04

Calculate Burger Production Rate

To find out how many burgers are produced per minute, divide the conveyor belt speed by the distance between the burgers. \[ \text{Burger Production Rate} = \frac{0.4286 \text{ m/min}}{0.25 \text{ m/burger}} = 1.7144 \text{ burgers/min} \]
05

Round Off the Production Rate

Since the rate must be in whole burgers per minute, we approximate the calculated rate. Thus, around 1 burger is produced per minute.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Grilling Machine
Imagine a grilling machine like a tiny cooking station, where burgers travel on a conveyor belt to get grilled to perfection. The length of this machine is crucial because it determines how long the burgers are exposed to the heat source for cooking.
The machine in this scenario is 1.2 meters long. This implies that every burger will take some time to get from the start of the grill to the end. The time a burger spends here affects both the final product's quality and how quickly burgers can be served to waiting customers. Understanding the length and the speed of travel is key for computing how many burgers can be processed in a certain amount of time.
By knowing the given length of the grilling machine and the required cooking time, we can ensure each burger gets enough time at the right cooking temperature while maintaining efficiency and speed.
Burger Spacing
Burger spacing is the gap between consecutive burgers on the conveyor belt. In our example, this distance is 25 cm, or 0.25 meters. This spacing is important because it affects the conveyor speed and production rate.
When burgers are spaced correctly, they enter the grilling machine at the right intervals. If the spacing were too large, it would waste space and reduce production speed. If it's too small, it might lead to overlapping burgers, insufficient cooking, or overheating. Proper spacing ensures smooth operation.
Knowing the spacing also helps us calculate how often new burgers can enter the grilling machine, which directly influences how many burgers can be produced in a given time.
Production Rate
The production rate reflects how many burgers the system can produce per minute. It hinges mainly on the speed of the conveyor and the spacing of the burgers.
To calculate this, divide the conveyor speed by the burger spacing, which in our case is 0.4286 meters per minute divided by 0.25 meters per burger. This calculation results in approximately 1.7144 burgers per minute.
However, since we can't produce a fraction of a burger, we round this number to the nearest whole number. Therefore, the practical production rate is about 1 burger per minute. This production rate helps in planning serving times and understanding the grilling system's efficiency.
Cooking Time
Cooking time is a key factor in ensuring that burgers are cooked through safely and thoroughly. In this example, it is agreed that each burger needs 2.8 minutes at the grilling machine.
The time required is determined by the length of the grilling machine and the speed at which the conveyor moves. Here, the conveyor belt speed was set so that the burgers spend exactly 2.8 minutes in the grilling area.
Cooking time ensures that the burgers reach a safety and quality standard, preventing raw centers and ensuring even cooking. Understanding this can also help adjust production rates if the speed or length of the grill is changed.

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