Answer :
Sure! Here is a step-by-step solution for each part of the question:
### Part 1: Rate Calculations
1. a) Km per litre:
- You travel 220 km on 20 litres of petrol.
- To find km per litre, divide the distance by the litres:
[tex]\[
\frac{220 \text{ km}}{20 \text{ litres}} = 11 \text{ km/litre}
\][/tex]
1. b) Cost per ticket:
- The total cost is R144 for 12 tickets.
- To find the cost per ticket, divide the total cost by the number of tickets:
[tex]\[
\frac{R144}{12} = R12 \text{ per ticket}
\][/tex]
1. c) Cars per hour:
- 560 cars in 8 hours.
- To find the number of cars per hour, divide the total number of cars by the hours:
[tex]\[
\frac{560 \text{ cars}}{8 \text{ hours}} = 70 \text{ cars/hour}
\][/tex]
1. d) Rands per hour:
- R60 for 6 hours.
- To find the cost per hour, divide the total cost by the hours:
[tex]\[
\frac{R60}{6} = R10 \text{ per hour}
\][/tex]
1. e) Cost per kg:
- R15.50 for 5 kg.
- To find the cost per kg, divide the total cost by the weight in kg:
[tex]\[
\frac{R15.50}{5 \text{ kg}} = R3.10 \text{ per kg}
\][/tex]
1. ก) Hours per day:
- 35 hours a week (5 days).
- To find hours per day, divide the total hours by the number of days:
[tex]\[
\frac{35 \text{ hours}}{5 \text{ days}} = 7 \text{ hours/day}
\][/tex]
1. g) Minutes per patient:
- 8 patients in 2 hours.
- Convert hours to minutes: 2 hours = 120 minutes.
- To find minutes per patient, divide the total minutes by the number of patients:
[tex]\[
\frac{120 \text{ minutes}}{8 \text{ patients}} = 15 \text{ minutes/patient}
\][/tex]
### Part 2: Thami and Norah
2. a) Cost per litre of paint:
- Thami buys 5 litres of paint for R35.
- To find the cost per litre, divide the total cost by the litres of paint:
[tex]\[
\frac{R35}{5 \text{ litres}} = R7.00 \text{ per litre}
\][/tex]
2. b) Norah's pay per hour:
- Norah is paid R175 per day for working from 09:00 to 16:00 (7 hours).
- To find pay per hour, divide the total pay by the number of hours:
[tex]\[
\frac{R175}{7 \text{ hours}} = R25.00 \text{ per hour}
\][/tex]
### Part 3: Speeds and Distances
3. a) Car speed in km/h:
- A car travels 220 km in 2 hours.
- To find the speed in km/h, divide the distance by the time:
[tex]\[
\frac{220 \text{ km}}{2 \text{ hours}} = 110 \text{ km/h}
\][/tex]
3. b) Distance traveled at constant speed:
- Driving at a constant speed of 90 km/h for 3 hours.
- To find the distance traveled, multiply the speed by the time:
[tex]\[
90 \text{ km/h} \times 3 \text{ hours} = 270 \text{ km}
\][/tex]
3. c) Taxi travel distance per hour:
- A taxi travels 120 km in 6 hours.
- To find the distance per hour, divide the distance by the hours:
[tex]\[
\frac{120 \text{ km}}{6 \text{ hours}} = 20 \text{ km/hour}
\][/tex]
### Part 4: Distance over Time Table
- A car travels at a constant speed of 120 km/h.
- To find the distances for given times (in minutes), convert minutes to hours and multiply by speed.
[tex]\[
\begin{align*}
60 \text{ min} & : \frac{60}{60} \times 120 = 120 \text{ km} \\
90 \text{ min} & : \frac{90}{60} \times 120 = 180 \text{ km} \\
120 \text{ min} & : \frac{120}{60} \times 120 = 240 \text{ km} \\
180 \text{ min} & : \frac{180}{60} \times 120 = 360 \text{ km} \\
240 \text{ min} & : \frac{240}{60} \times 120 = 480 \text{ km}
\end{align*}
\][/tex]
### Part 5: Study Table
5. a) Fill in the missing distances:
- A vehicle travels with a constant speed (found in part 5.b):
- For each hour from 2 to 6, add the speed multiplied by time difference to 180 km.
[tex]\[
\begin{align*}
\text{3 hours} & : 180 + (120 \times (3-2)) = 300 \text{ km} \\
\text{4 hours} & : 300 + (120 \times (4-3)) = 420 \text{ km} \\
\text{5 hours} & : 420 + (120 \times (5-4)) = 540 \text{ km} \\
\text{6 hours} & : 540 + (120 \times (6-5)) = 660 \text{ km}
\end{align*}
\][/tex]
5. b) Vehicle Speed:
- The speed of the vehicle can be calculated by using the distance and time (from given initial values):
[tex]\[
\frac{180 \text{ km}}{2 \text{ hours}} = 90 \text{ km/h}
\][/tex]
### Part 6: Fuel Consumption
- Car uses 10 litres per 100 km.
- To find the fuel needed for each distance, multiply the distance by the litre used per 100 km and divide by 100.
[tex]\[
\begin{align*}
50 \text{ km} & : \frac{50 \times 10}{100} = 5 \text{ litres} \\
75 \text{ km} & : \frac{75 \times 10}{100} = 7.5 \text{ litres} \\
100 \text{ km} & : \frac{100 \times 10}{100} = 10 \text{ litres} \\
150 \text{ km} & : \frac{150 \times 10}{100} = 15 \text{ litres} \\
200 \text{ km} & : \frac{200 \times 10}{100} = 20 \text{ litres}
\end{align*}
\][/tex]
I hope this helps you understand how to solve each part step-by-step! If you have any questions or need further clarification, feel free to ask!
### Part 1: Rate Calculations
1. a) Km per litre:
- You travel 220 km on 20 litres of petrol.
- To find km per litre, divide the distance by the litres:
[tex]\[
\frac{220 \text{ km}}{20 \text{ litres}} = 11 \text{ km/litre}
\][/tex]
1. b) Cost per ticket:
- The total cost is R144 for 12 tickets.
- To find the cost per ticket, divide the total cost by the number of tickets:
[tex]\[
\frac{R144}{12} = R12 \text{ per ticket}
\][/tex]
1. c) Cars per hour:
- 560 cars in 8 hours.
- To find the number of cars per hour, divide the total number of cars by the hours:
[tex]\[
\frac{560 \text{ cars}}{8 \text{ hours}} = 70 \text{ cars/hour}
\][/tex]
1. d) Rands per hour:
- R60 for 6 hours.
- To find the cost per hour, divide the total cost by the hours:
[tex]\[
\frac{R60}{6} = R10 \text{ per hour}
\][/tex]
1. e) Cost per kg:
- R15.50 for 5 kg.
- To find the cost per kg, divide the total cost by the weight in kg:
[tex]\[
\frac{R15.50}{5 \text{ kg}} = R3.10 \text{ per kg}
\][/tex]
1. ก) Hours per day:
- 35 hours a week (5 days).
- To find hours per day, divide the total hours by the number of days:
[tex]\[
\frac{35 \text{ hours}}{5 \text{ days}} = 7 \text{ hours/day}
\][/tex]
1. g) Minutes per patient:
- 8 patients in 2 hours.
- Convert hours to minutes: 2 hours = 120 minutes.
- To find minutes per patient, divide the total minutes by the number of patients:
[tex]\[
\frac{120 \text{ minutes}}{8 \text{ patients}} = 15 \text{ minutes/patient}
\][/tex]
### Part 2: Thami and Norah
2. a) Cost per litre of paint:
- Thami buys 5 litres of paint for R35.
- To find the cost per litre, divide the total cost by the litres of paint:
[tex]\[
\frac{R35}{5 \text{ litres}} = R7.00 \text{ per litre}
\][/tex]
2. b) Norah's pay per hour:
- Norah is paid R175 per day for working from 09:00 to 16:00 (7 hours).
- To find pay per hour, divide the total pay by the number of hours:
[tex]\[
\frac{R175}{7 \text{ hours}} = R25.00 \text{ per hour}
\][/tex]
### Part 3: Speeds and Distances
3. a) Car speed in km/h:
- A car travels 220 km in 2 hours.
- To find the speed in km/h, divide the distance by the time:
[tex]\[
\frac{220 \text{ km}}{2 \text{ hours}} = 110 \text{ km/h}
\][/tex]
3. b) Distance traveled at constant speed:
- Driving at a constant speed of 90 km/h for 3 hours.
- To find the distance traveled, multiply the speed by the time:
[tex]\[
90 \text{ km/h} \times 3 \text{ hours} = 270 \text{ km}
\][/tex]
3. c) Taxi travel distance per hour:
- A taxi travels 120 km in 6 hours.
- To find the distance per hour, divide the distance by the hours:
[tex]\[
\frac{120 \text{ km}}{6 \text{ hours}} = 20 \text{ km/hour}
\][/tex]
### Part 4: Distance over Time Table
- A car travels at a constant speed of 120 km/h.
- To find the distances for given times (in minutes), convert minutes to hours and multiply by speed.
[tex]\[
\begin{align*}
60 \text{ min} & : \frac{60}{60} \times 120 = 120 \text{ km} \\
90 \text{ min} & : \frac{90}{60} \times 120 = 180 \text{ km} \\
120 \text{ min} & : \frac{120}{60} \times 120 = 240 \text{ km} \\
180 \text{ min} & : \frac{180}{60} \times 120 = 360 \text{ km} \\
240 \text{ min} & : \frac{240}{60} \times 120 = 480 \text{ km}
\end{align*}
\][/tex]
### Part 5: Study Table
5. a) Fill in the missing distances:
- A vehicle travels with a constant speed (found in part 5.b):
- For each hour from 2 to 6, add the speed multiplied by time difference to 180 km.
[tex]\[
\begin{align*}
\text{3 hours} & : 180 + (120 \times (3-2)) = 300 \text{ km} \\
\text{4 hours} & : 300 + (120 \times (4-3)) = 420 \text{ km} \\
\text{5 hours} & : 420 + (120 \times (5-4)) = 540 \text{ km} \\
\text{6 hours} & : 540 + (120 \times (6-5)) = 660 \text{ km}
\end{align*}
\][/tex]
5. b) Vehicle Speed:
- The speed of the vehicle can be calculated by using the distance and time (from given initial values):
[tex]\[
\frac{180 \text{ km}}{2 \text{ hours}} = 90 \text{ km/h}
\][/tex]
### Part 6: Fuel Consumption
- Car uses 10 litres per 100 km.
- To find the fuel needed for each distance, multiply the distance by the litre used per 100 km and divide by 100.
[tex]\[
\begin{align*}
50 \text{ km} & : \frac{50 \times 10}{100} = 5 \text{ litres} \\
75 \text{ km} & : \frac{75 \times 10}{100} = 7.5 \text{ litres} \\
100 \text{ km} & : \frac{100 \times 10}{100} = 10 \text{ litres} \\
150 \text{ km} & : \frac{150 \times 10}{100} = 15 \text{ litres} \\
200 \text{ km} & : \frac{200 \times 10}{100} = 20 \text{ litres}
\end{align*}
\][/tex]
I hope this helps you understand how to solve each part step-by-step! If you have any questions or need further clarification, feel free to ask!
