We are given the following information:

• A teacher can grade 27 tests in 3 hours.
• We are asked to find how many tests the teacher can grade in 8 hours if they continue grading at the same rate.

Step 1: Calculate the rate of grading per hour

The teacher's grading rate is: $\frac{27 \text{ tests}}{3 \text{ hours}} = 9 \text{ tests per hour}.$

Step 2: Multiply the rate by the number of hours

Now, to find out how many tests the teacher can grade in 8 hours: $9 \text{ tests/hour} \times 8 \text{ hours} = 72 \text{ tests}.$

Thus, the teacher can grade 72 tests in 8 hours.

Would you like more details or have any questions?

Here are five related questions for further practice:

1. If the teacher grades 40 tests in 5 hours, how many tests per hour is this?
2. How long will it take the teacher to grade 100 tests at the rate of 9 tests per hour?
3. If the teacher increases their grading speed to 12 tests per hour, how many tests will they grade in 7 hours?
4. How many tests can the teacher grade in 10 hours if the rate decreases to 8 tests per hour?
5. A different teacher can grade 35 tests in 5 hours. How does this rate compare to the first teacher’s rate?

Tip: When dealing with proportional relationships, always check the rate and multiply by the desired time or quantity to find the result.