Practice Maths

Understanding and Graphing Rates — Solutions

Click any answer to watch the solution video.

  1. Calculate the unit rate

    1. $45 for 9 kg:
    2. 240 km on 8 L:
    3. $72 for 6 hours:
    4. 350 words in 5 min:
    5. $3.60 for 4 oranges:
    6. 180 L in 9 min:
    7. $84 for 12 kg:
    8. 630 km in 7 hours:

  2. Use the given rate to calculate the quantity

    1. 60 km/h for 2.5 h:
    2. $8.50/kg × 4 kg:
    3. 25 L/min × 6 min:
    4. $22/h × 8 h:
    5. 9 L/100 km for 250 km:
    6. 200 km at 80 km/h:
    7. $90 ÷ $12/kg:
    8. 90 pages ÷ 15 pages/min:

  3. Convert each rate

    1. 1.5 L/min to L/hour:
    2. 120 km/h to km/min:
    3. $3/min to $/hour:
    4. 500 mL/min to L/hour:
    5. 72 km/h to m/s:
    6. $600/day to $/hour (8-hr day):
    7. 2 m/s to m/min:
    8. 45 L/hour to L/min:

  4. Interpret rates from graphs

    1. (0,0) to (3,180):
    2. (0,0) to (5,200):
    3. (0,0) to (4,22):
    4. Horizontal line:
    5. Line A (2,100) vs Line B (2,60):
    6. Starting point (0,50):
    7. (0,0) to (5, 87.50):
    8. (0,80) to (4,0):

  5. Compare rates — better value

    1. Store A $0.60/banana, Store B $0.64/banana:
    2. Plan A $9/GB, Plan B $7.75/GB:
    3. 8 L/100 km vs 12 L/100 km:
    4. Job A $18/h, Job B $15/h:
    5. Recipe A 16.7 g/biscuit, Recipe B 15 g/biscuit:
    6. Swimmer A 50 m/min, Swimmer B 50 m/min:

  6. Multi-step rate problems

    1. Total distance and average speed:
    2. Sam’s total earnings:
    3. Pool fill time:
    4. Fuel cost:
    5. Tank fill time with leak:

  7. Identify the rate — correct notation

    1. 8 L per 100 km driven:
    2. 120 boxes in 4 hours:
    3. 5 litres per 2 hours:
    4. 600 items per 8-hour shift:
    5. 400 m in 50 s:
    6. 250 g flour per loaf:

  8. Distance–time graph: three lines

    1. Speed of Line P:
    2. Speed of Line Q:
    3. Speed of Line R:
    4. Fastest line:
    5. Same distance after 4 h:
    6. Steepness meaning:

  9. Fuel consumption context

    1. Fuel for 300 km:
    2. Total fuel cost:
    3. Distance on 50 L:
    4. Max distance under $50:

  10. Challenging rate problems

    1. Total journey time:
    2. Tap B alone:
    3. Third-hour distance:
    4. Time to print 2000 pages: