Subjects algebra

Constant Speed

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Constant Speed


1. **Problem 4.1** involves understanding Moshe's constant speed from the table and answering related questions. 2. **Given table for travel:** Hours: 2, 3, 4, 5, 9, 10, 12, 15 Kilometres: 160, 240, 320, 600, 740, __, 960, 1200 3. **Step a: Find constant speed** Speed is distance divided by time. Let's check if speed is constant by calculating speed for known pairs: - At 2 hours: Speed = $\frac{160}{2} = 80$ km/h - At 3 hours: Speed = $\frac{240}{3} = 80$ km/h - At 4 hours: Speed = $\frac{320}{4} = 80$ km/h So, speed appears to be 80 km/h where data is consistent. 4. **Step b: Complete missing km at 10 hours:** At 10 hours: $80 \times 10 = 800$ km 5. **Step c: Use this speed to answer graph questions:** i) After 6 hours: Distance = $80 \times 6 = 480$ km ii) After 18 hours: Distance = $80 \times 18 = 1440$ km iii) Time to cover 640 km: $\frac{640}{80} = 8$ hours iv) Time to cover 280 km: $\frac{280}{80} = 3.5$ hours 6. **Step d: Driving all day with only 1 hour lunch break** Assuming 24 hours in a day, driving time = $24 - 1 = 23$ hours Distance covered = $80 \times 23 = 1840$ km --- 7. **Problem 4.2** involves calculating price per litre from the milk table: Litres: 3, 5, 6, 7, 8, 9, 11, 12 Price: 12, 20, __, __, __, __, 44, __ 8. Find unit price: For 3 litres at 12 rands, price per litre = $\frac{12}{3} = 4$ rands/litre Check for 5 litres at 20 rands: $\frac{20}{5} = 4$ rands/litre matches 9. Complete missing prices: - 6 litres: $6 \times 4 = 24$ rands - 7 litres: $7 \times 4 = 28$ rands - 8 litres: $8 \times 4 = 32$ rands - 9 litres: $9 \times 4 = 36$ rands - 12 litres: $12 \times 4 = 48$ rands 10. Confirm 11 litres price: $44$ rands is given. Expected at 4 rands/litre is $11 \times 4=44$, so consistent **Final answers:** - Constant speed = $80$ km/h - Missing km at 10 hours = $800$ km - Distances after 6 and 18 hours: $480$ km and $1440$ km - Times for 640 km and 280 km: $8$ hours and $3.5$ hours - Distance in a day with 1-hour lunch: $1840$ km - Milk price per litre = $4$ rands/litre - Completed price table for milk: 24, 28, 32, 36, 44, 48 rands