Worksheet for calculating unit rates with real-world scenarios.

Let's solve each problem step by step, focusing on finding unit rates — that is, determining how much of something happens per unit of time (like per minute or per hour). We'll convert the given rates to a common time unit (usually per hour) and then compute the final answer.

---

Problem 1

> Andrew works in an assembly line at a toy manufacturing factory. This morning, he assembled 3 toys in 30 minutes. Assuming he continues working at the same rate, how many toys can he assemble in an hour?

#### Step-by-step:
- He assembles 3 toys in 30 minutes.
- There are 60 minutes in an hour, so we need to find how many toys he makes in 60 minutes.
- Since 60 minutes is twice 30 minutes, we double the number of toys:
$$
3 \text{ toys} \times 2 = 6 \text{ toys}
$$

✔ Answer: 6 toys

---

Problem 2

> José stuffs envelopes as a part-time job on weekends. He stuffs 24 envelopes in 20 minutes. If he continues to stuff envelopes at this constant rate, how many envelopes can he stuff per hour?

#### Step-by-step:
- He stuffs 24 envelopes in 20 minutes.
- First, find how many envelopes per minute:
$$
\frac{24}{20} = 1.2 \text{ envelopes per minute}
$$
- Now multiply by 60 minutes in an hour:
$$
1.2 \times 60 = 72 \text{ envelopes}
$$

Alternatively, use proportion:
- 20 minutes → 24 envelopes
- 60 minutes → ? envelopes
$$
\frac{24}{20} = \frac{x}{60} \Rightarrow x = \frac{24 \times 60}{20} = 72
$$

✔ Answer: 72 envelopes

---

Problem 3

> A recycling plant processes $ \frac{1}{4} $ ton of paper every 3 minutes. If the plant operates at a constant rate, how many tons of paper does the recycling plant process in 1 hour?

#### Step-by-step:
- It processes $ \frac{1}{4} $ ton every 3 minutes.
- First, find how many 3-minute intervals are in 60 minutes:
$$
\frac{60}{3} = 20 \text{ intervals}
$$
- So, in one hour, it processes:
$$
20 \times \frac{1}{4} = \frac{20}{4} = 5 \text{ tons}
$$

✔ Answer: 5 tons

---

Problem 4

> Tyler conducted a scientific experiment by mixing 2 liquids. The temperature of the liquids rose 1.5 degrees in 4 minutes. Continuing at this rate, what would be the increase in the temperature of the liquid in 1 hour?
> Write your answer as a mixed number, simplified fraction, or an exact decimal.

#### Step-by-step:
- Temperature increases 1.5 degrees in 4 minutes.
- Find how many 4-minute intervals are in 60 minutes:
$$
\frac{60}{4} = 15 \text{ intervals}
$$
- So total increase in 1 hour:
$$
15 \times 1.5 = 22.5 \text{ degrees}
$$

Or using fractions:
- $ 1.5 = \frac{3}{2} $
- $ 15 \times \frac{3}{2} = \frac{45}{2} = 22.5 $

As a mixed number: $ 22\frac{1}{2} $

✔ Answer: $ 22.5 $ or $ 22\frac{1}{2} $ degrees

---

✔ Final Answers:

1. 6 toys
2. 72 envelopes
3. 5 tons
4. $ 22.5 $ or $ 22\frac{1}{2} $ degrees

Let me know if you'd like these explained visually or with diagrams!