Final answer:
The conveyor belt must travel at a speed of approximately 0.5772 meters per minute to cook the burgers, and the rate of burger production is approximately 3.848 burgers per minute when they are spaced 15 cm apart.
Step-by-step explanation:
To calculate the speed at which the conveyor belt must travel to cook the burgers, we first need to convert the cooking time from minutes to seconds. Since the burgers require 2.6 minutes to cook, this translates to 2.6 × 60 = 156 seconds. As the grilling machine is 1.5 meters long, we divide this distance by the time to get the speed:
Speed = Distance / Time = 1.5 meters / 156 seconds ≈ 0.00962 meters per second.
To express this in meters per minute, we multiply by 60:
Speed = 0.00962 meters per second × 60 = 0.5772 meters per minute.
Now, to find the rate of burger production, given that the burgers are spaced 15 cm (or 0.15 meters) apart, we determine how many burgers will be produced per minute. This is the inverse of the spacing in meters divided by the speed of the belt:
Rate of burger production = 1 / (0.15 meters / 0.5772 meters per minute) ≈ 3.848 burgers per minute.