Grade 7 Mathematics Worksheet on Rate Problems - Sample Page

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Let’s go through each question step-by-step:

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Question 1.1:

If a car travels at 125 km/h, how far will it travel in 4½ hours?

Solution:

We use the formula:
> Distance = Rate × Time

- Rate = 125 km/h
- Time = 4½ hours = 4.5 hours

$$
\text{Distance} = 125 \times 4.5 = 562.5 \text{ km}
$$

✔ Answer: The car will travel 562.5 km.

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Question 1.2:

The hot dog eating champion of the world ate 74 hot dogs in 10 minutes. What is the rate of hot dogs per minute?

Solution:

We divide total hot dogs by time in minutes:

$$
\text{Rate} = \frac{74}{10} = 7.4 \text{ hot dogs per minute}
$$

✔ Answer: The rate is 7.4 hot dogs per minute.

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Question 1.3:

Angelo paints 75 m² of the wall in 3 hours. How many square meters will he paint in 5 hours?

Step 1: Find his painting rate (m² per hour)

$$
\text{Rate} = \frac{75}{3} = 25 \text{ m²/hour}
$$

Step 2: Multiply by 5 hours

$$
\text{Area} = 25 \times 5 = 125 \text{ m²}
$$

✔ Answer: Angelo will paint 125 m² in 5 hours.

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Question 1.4:

Jerome's heart beats 234 times in 3 minutes. Another person's heart beats 180 times in 5 minutes. Who has the slowest heart rate?

Step 1: Calculate Jerome’s heart rate (beats per minute)

$$
\frac{234}{3} = 78 \text{ bpm (beats per minute)}
$$

Step 2: Calculate the other person’s heart rate

$$
\frac{180}{5} = 36 \text{ bpm}
$$

Compare:
- Jerome: 78 bpm
- Other: 36 bpm

✔ Answer: The second person (with 36 bpm) has the slowest heart rate.

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Question 1.5:

A Porsche Macan has a fuel consumption of 8.7 L/100 km and CO₂ emissions of 159 g/km. A Ferrari has a fuel consumption of 12.9 L/100 km and CO₂ emissions of 288 g/km.

#### a) Which vehicle is the least fuel-efficient?

- Porsche: 8.7 L/100 km
- Ferrari: 12.9 L/100 km

Higher fuel consumption = less efficient

✔ Answer: The Ferrari is the least fuel-efficient.

#### b) Which vehicle is the most environmentally friendly?

Lower CO₂ emissions = more eco-friendly

- Porsche: 159 g/km
- Ferrari: 288 g/km

✔ Answer: The Porsche is more environmentally friendly.

#### c) If you drove the Porsche Macan at constant speed for 300 km, how much fuel do you expect to use?

Use proportion:

$$
\frac{8.7 \text{ L}}{100 \text{ km}} = \frac{x}{300 \text{ km}}
$$

$$
x = \frac{8.7 \times 300}{100} = 26.1 \text{ L}
$$

✔ Answer: You would use 26.1 litres of fuel.

#### d) If you drove the Ferrari at constant speed for 550 km, how many grams of CO₂ do you expect to emit?

CO₂ emission rate: 288 g/km

$$
\text{Total CO₂} = 288 \times 550 = 158,400 \text{ grams}
$$

✔ Answer: You would emit 158,400 grams of CO₂.

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✔ Final Answers Summary:

| Question | Answer |
|--------|--------|
| 1.1 | 562.5 km |
| 1.2 | 7.4 hot dogs per minute |
| 1.3 | 125 m² |
| 1.4 | The person with 180 beats in 5 minutes (36 bpm) has the slowest heart rate |
| 1.5a | Ferrari (least fuel-efficient) |
| 1.5b | Porsche (more environmentally friendly) |
| 1.5c | 26.1 litres |
| 1.5d | 158,400 grams of CO₂ |

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