#### Answer

The belt moves at a speed of 0.43 meters per minute. The rate of burger production is 1.7 burgers/minute.

#### Work Step by Step

We first find the required speed of the conveyor belt:
$v = \frac{x}{t}$
$v = \frac{1.2 ~m}{2.8 ~min}$
$v = 0.43 ~m/min$
We can then find the number of burgers $N$ on the 1.2-meter belt:
$N = \frac{1.2~m}{0.25~m} = 4.8~burgers$
On average, 4.8 burgers will be cooked every 2.8 minutes. We can find the rate of burger production in units of burgers/minute:
$rate = \frac{4.8~burgers}{2.8~min} = 1.7 ~burgers/min$
The belt moves at a speed of 0.43 meters per minute. The rate of burger production is 1.7 burgers/minute.