Sample Grade 9 Math worksheet on Rate, Ratio, and Proportion from StudyChamp.co.za.

Problem Analysis and Solution

The provided worksheet focuses on Rate, Ratio, and Proportion. Let's solve each question step by step.

---

#### Question 1: Fill in the missing numbers

##### 1.1 Jamie’s heart beats 136 times in two minutes. His heart rate is ______ beats per minute.
- Given: Jamie’s heart beats 136 times in 2 minutes.
- To find: Heart rate in beats per minute (bpm).
- Solution:
\[
\text{Heart rate} = \frac{\text{Total beats}}{\text{Time in minutes}} = \frac{136}{2} = 68 \text{ bpm}
\]
- Answer: 68

##### 1.2 The cyclist cycles at ______ km/h. She will cover ______ km in 4 hours.
- Given: The cyclist cycles for 4 hours.
- To find: Speed in km/h and distance covered in 4 hours.
- Assumption: Since the speed is not given, let’s denote the speed as \( v \) km/h.
- Distance formula:
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
If the speed is \( v \) km/h, then the distance covered in 4 hours is:
\[
\text{Distance} = v \times 4
\]
- Answer: The speed is \( v \) km/h, and the distance covered is \( 4v \) km. Without a specific speed, these are the general expressions.

##### 1.3 The factory produces 5,750 plastic bottles in 20 minutes. Its production rate is ______ bottles/hr.
- Given: The factory produces 5,750 bottles in 20 minutes.
- To find: Production rate in bottles per hour.
- Solution:
- First, convert 20 minutes to hours:
\[
20 \text{ minutes} = \frac{20}{60} \text{ hours} = \frac{1}{3} \text{ hours}
\]
- Production rate:
\[
\text{Production rate} = \frac{\text{Total bottles}}{\text{Time in hours}} = \frac{5,750}{\frac{1}{3}} = 5,750 \times 3 = 17,250 \text{ bottles/hr}
\]
- Answer: 17,250

##### 1.4 After the race, Mandy’s heart rate was 168 beats/min. This was ______ beats/sec.
- Given: Mandy’s heart rate is 168 beats per minute.
- To find: Heart rate in beats per second.
- Solution:
- Convert beats per minute to beats per second:
\[
\text{Beats per second} = \frac{\text{Beats per minute}}{60} = \frac{168}{60} = 2.8 \text{ beats/sec}
\]
- Answer: 2.8

##### 1.5 The tiler tiled 48 m² in 8.5 hours. He will take ______ hours and ______ minutes to tile 72 m².
- Given: The tiler tiles 48 m² in 8.5 hours.
- To find: Time required to tile 72 m².
- Solution:
- First, find the tiling rate:
\[
\text{Tiling rate} = \frac{\text{Area tiled}}{\text{Time}} = \frac{48 \text{ m}^2}{8.5 \text{ hours}} \approx 5.647 \text{ m}^2/\text{hour}
\]
- Time required to tile 72 m²:
\[
\text{Time} = \frac{\text{Area to tile}}{\text{Tiling rate}} = \frac{72}{5.647} \approx 12.75 \text{ hours}
\]
- Convert 0.75 hours to minutes:
\[
0.75 \text{ hours} \times 60 \text{ minutes/hour} = 45 \text{ minutes}
\]
- Total time: 12 hours and 45 minutes.
- Answer: 12 hours and 45 minutes

---

#### Question 2: Complete the following table calculations as requested

##### 2.1 Table Completion
The table relates the volume of bottled water, cost per container, and cost per litre. We need to fill in the missing values.

| Bottled Water | Cost per Container | Cost per Litre |
|---------------|---------------------|----------------|
| 250 ml | | R26.00 |
| 900 ml | R12.25 | |
| | R16.50 | R11.00 |
| 5 litres | R38.50 | |

- Row 1: 250 ml, Cost per Litre = R26.00
- Volume in litres: \( 250 \text{ ml} = 0.25 \text{ litres} \)
- Cost per container:
\[
\text{Cost per container} = \text{Cost per litre} \times \text{Volume in litres} = 26 \times 0.25 = R6.50
\]

- Row 2: 900 ml, Cost per Container = R12.25
- Volume in litres: \( 900 \text{ ml} = 0.9 \text{ litres} \)
- Cost per litre:
\[
\text{Cost per litre} = \frac{\text{Cost per container}}{\text{Volume in litres}} = \frac{12.25}{0.9} \approx R13.61
\]

- Row 3: Cost per Container = R16.50, Cost per Litre = R11.00
- Volume in litres:
\[
\text{Volume in litres} = \frac{\text{Cost per container}}{\text{Cost per litre}} = \frac{16.50}{11.00} = 1.5 \text{ litres}
\]
- Bottled Water: 1,500 ml (since 1.5 litres = 1,500 ml)

- Row 4: 5 litres, Cost per Container = R38.50
- Cost per litre:
\[
\text{Cost per litre} = \frac{\text{Cost per container}}{\text{Volume in litres}} = \frac{38.50}{5} = R7.70
\]

Completed Table:

| Bottled Water | Cost per Container | Cost per Litre |
|---------------|---------------------|----------------|
| 250 ml | R6.50 | R26.00 |
| 900 ml | R12.25 | R13.61 |
| 1,500 ml | R16.50 | R11.00 |
| 5 litres | R38.50 | R7.70 |

##### 2.2 Formula to calculate the volume of water if the cost per litre and per container are known
- Given: Cost per litre (\( C_L \)) and Cost per container (\( C_C \)).
- To find: Volume of water in the container (\( V \)).
- Formula:
\[
V = \frac{\text{Cost per container}}{\text{Cost per litre}} = \frac{C_C}{C_L}
\]

Final Answer:
\[
\boxed{V = \frac{C_C}{C_L}}
\]

---

Final Answers Summarized

1.1: 68
1.2: Speed \( v \) km/h, Distance \( 4v \) km
1.3: 17,250
1.4: 2.8
1.5: 12 hours and 45 minutes
2.1:
- Row 1: R6.50
- Row 2: R13.61
- Row 3: 1,500 ml
- Row 4: R7.70
2.2: \( V = \frac{C_C}{C_L} \)

Boxed Final Answer for Question 2.2:
\[
\boxed{V = \frac{C_C}{C_L}}
\]