To solve this, we can use a proportion based on the rate of the grading machine. The machine can grade 96 tests in 2 minutes. If the teacher has 300 tests to grade, we need to find out how many minutes it will take.

We can set up the proportion as:

$\frac{96 \, \text{tests}}{2 \, \text{minutes}} = \frac{300 \, \text{tests}}{x \, \text{minutes}}$

Cross-multiply and solve for $x$:

$96x = 2 \times 300$

$96x = 600$

Now, divide both sides by 96:

$x = \frac{600}{96} = 6.25$

So, it will take the machine 6.25 minutes to grade 300 tests.

Would you like any further details or clarification?

Here are 5 related questions:

1. How many tests can the machine grade in 1 minute?
2. If the machine's speed doubles, how long will it take to grade the 300 tests?
3. How long would it take to grade 450 tests at the same speed?
4. If the machine only graded 80 tests in 2 minutes, how long would it take for 300 tests?
5. How many tests could the machine grade in 10 minutes?

Tip: When solving rate problems, setting up proportions helps simplify the calculation.