Year 8 Mathematics | Victorian Curriculum 2.0
Rates
Topic 12 | Measurement & Space | Answer key

Year 8 core - answers

Fluency

Unit rates

    1. 6060 km/h
    2. 3030 L/min
    3. $27/h
    4. 99 g/cm3^3
    5. 1515 pages/min
Fluency

Speed, distance, time

    1. 195195 km
    2. 66 h
    3. 88 m/s
    4. 2020 m/s. Method: 72×1000360072 \times \tfrac{1000}{3600}.
    5. 11 h 3030 min
    6. 160160 km/h. Method: 400÷2.5400 \div 2.5.
Fluency

Fuel, pay, exchange

    1. 2828 L. Method: 8100×350\tfrac{8}{100} \times 350.
    2. $803. Method: 22×36.522 \times 36.5.
    3. $127.50 NZD. Method: 150×0.85150 \times 0.85.
    4. $300 AUD. Method: 200×1.50200 \times 1.50.
    5. $120 interest. Method: 4100×1000×3\tfrac{4}{100} \times 1000 \times 3.
Reasoning

Explain and spot the mistake

    1. Units km/hour (or km per hour). Sam dropped the “per hour” and collapsed the rate to a distance, losing the time dimension. Correct: 5050 km/h.
    2. Same speed. B does 3030 km in 0.50.5 h =60= 60 km/h.
    3. A rate is any comparison of two different quantities (e.g. 6060 km in 1.51.5 h). A unit rate is the per-one-unit form (e.g. 4040 km/h). A rate can be simplified to a unit rate by division.
    4. 10×20=20010 \times 20 = 200 L vs 4×60=2404 \times 60 = 240 L. The second delivers more.
Problem solving

Real contexts

    1. 1616 h. Method: 1600÷1001600 \div 100.
    2. 10001000 min ≈16\approx 16 h 4040 min.
    3. Single pen is dearer by 1010 c each. Box price =30= 30 c/pen; individual 4040 c/pen; difference 1010 c.
    4. B beats A when 25+0.10m>3525 + 0.10 m > 35, i.e. m>100m > 100 minutes.
    5. Copper 2525 kg, tin 1515 kg. Method: 5+3=85 + 3 = 8 parts; each part =5= 5 kg.

Challenge - answers

Reasoning

Harder problems

    1. 6868 km/h. Method: total distance =160+180=340= 160 + 180 = 340 km; total time =5= 5 h; 340/5340/5.
    2. 25%25\%. Method: profit =3= 3 dollars/kg; 3/123/12.
    3. 120120 min. Method: net 55 L/min; 600/5600/5.
    4. Yes, small profit. $100 AUD → $65 USD → $52 EUR → $83.20 AUD. Wait: that’s a loss. Let me redo - actually the chain gives 100×0.65×0.80×1.60=83.20100 \times 0.65 \times 0.80 \times 1.60 = 83.20 AUD, so a loss, not a profit. No arbitrage exists; the student has lost $16.80 on fees-free conversion.
Year 8 Mathematics study companion | Answer key