Percentages and ratio · Ages 13–14

Average speed and mixtures worksheet

Part of: Rates, ratios & proportions

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Percentages and ratio · Ages 13–14

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.3 kg of rice at $12 a kg is mixed with 2 kg at $60 a kg. The total price is $, an average of $ a kg.
Fill in each blank
Answer:
2.A car drives 1 hours at 90 km/h, then 1 hours at 50 km/h. Its average speed for the whole trip = km/h
Answer:
3.A car drives 2 hours at 80 km/h, then 2 hours at 90 km/h. Its average speed for the whole trip = km/h
Answer:
4.There are 6 kg of sweets at $54 a kg. How many kg of sweets at $92 a kg must be added to make the mixture $91 a kg?
Answer:
5.Tea at $34 a kg is mixed with tea at $44 a kg to make a blend at $40 a kg. The weights (the $34 tea : the $44 tea) are :
Fill in each blank
Answer:
6.There are 8 kg of sweets at $24 a kg. How many kg of sweets at $116 a kg must be added to make the mixture $112 a kg?
Answer:
7.The first half of a trip is driven at 35 km/h. At what speed must the second half go for the average over the whole trip to be 45 km/h?
Answer:
8.The first half of a trip is driven at 60 km/h. At what speed must the second half go for the average over the whole trip to be 80 km/h?
Answer:

9.A car goes from P to Q at 90 km/h and comes back the same way at 10 km/h. What is its average speed for the whole trip?
- A. 50 km/h
- B. 18 km/h
- C. 100 km/h
- D. 80 km/h
Choose the right answer
Answer:
10.Going at 15 km/h and coming back the same way at 75 km/h, the average speed for the whole trip is 25 km/h.
True or false?
Answer:
11.A car goes from P to Q at 100 km/h and comes back the same way at 60 km/h. What is its average speed for the whole trip?
- A. 75 km/h
- B. 80 km/h
- C. 40 km/h
- D. 160 km/h
Choose the right answer
Answer:
12.Tsz-hin cycles 6 km in 0.5 hours, rests 60 minutes, then cycles 6 km in 1.5 hours. Counting the rest, what is the average speed for the whole trip?
- A. 3 km/h
- B. 6 km/h
- C. 8 km/h
- D. 4 km/h
Choose the right answer
Answer:

13.A tea shop blends teas costing $40 and $110 a kg in the ratio 2 : 1, and sells the blend at a 20% profit. What is its selling price per kg?
Working:
Answer:
14.Chi-keung runs for 20 minutes at 140 m a minute, then walks for 5 minutes at 120 m a minute. On average, how many metres a minute is that?
- A. 136 m
- B. 130 m
- C. 260 m
- D. 168013 m
Choose the right answer
Working:
Answer:
15.Ming's family drives from P to Q at an average of 30 km/h and back at 60 km/h, 6 hours in all. How far apart are P and Q?
Working:
Answer:
16.A café blends coffee beans at $32 and $112 a kg into 45 kg at $80 a kg on average. It takes kg of the $32 beans and kg of the $112 beans.
Fill in each blank
Working:
Answer:
17.Tsz-hin walks 2.4 km from home to the park in 36 minutes and runs back the same way in 28 minutes. That is km in all, over minutes, an average of m a minute.
Fill in each blank
Working:
Answer:
18.A shop mixes 20 kg of peanuts at $36 a kg with 30 kg at $38 a kg. What is the mixture's average cost per kg?
Working:
Answer:

Show the answers and working

Average speed and mixtures worksheet: Answers and working

1. 156, 31.2
Total price 12 × 3 + 60 × 2 = 156 over 5 kg: 156 ÷ 5 = 31.2.
2. 70
Total distance 90 × 1 + 50 × 1 = 140 km over 2 hours: 140 ÷ 2 = 70 km/h.
3. 85
Total distance 80 × 2 + 90 × 2 = 340 km over 4 hours: 340 ÷ 4 = 85 km/h.
4. 222 kg
Add x kg: 54 × 6 + 92x = 91(6 + x), so x = 6 × (91 − 54) ÷ (92 − 91) = 222.
5. 2, 3
$34 is 6 below the average and $44 is 4 above. The gains must cancel the losses: the weights are 4 : 6 = 2 : 3. Check: (34 × 2 + 44 × 3) ÷ (2 + 3) = 40.
6. 176 kg
Add x kg: 24 × 8 + 116x = 112(8 + x), so x = 8 × (112 − 24) ÷ (116 − 112) = 176.
7. 63 km/h
Say each half is d km: 2d ÷ (d35 + dx) = 45, so 1x = 245 − 135, and x = 63. Not 2 × 45 − 35.
8. 120 km/h
Say each half is d km: 2d ÷ (d60 + dx) = 80, so 1x = 280 − 160, and x = 120. Not 2 × 80 − 60.

9. B. 18 km/h
Say each way is d km: the time is d90 + d10, so the average speed = 2d ÷ (d90 + d10) = 2 × 90 × 10 ÷ (90 + 10) = 18 km/h.
10. True
Total distance ÷ total time: 2 × 15 × 75 ÷ (15 + 75) = 25 km/h, not the average of the speeds, 45.
11. A. 75 km/h
Say each way is d km: the time is d100 + d60, so the average speed = 2d ÷ (d100 + d60) = 2 × 100 × 60 ÷ (100 + 60) = 75 km/h.
12. D. 4 km/h
Total distance 6 + 6 km, total time 0.5 + 1 + 1.5 = 3 hours: 4 km/h.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 76 dollars
Cost per kg: (40 × 2 + 110 × 1) ÷ (2 + 1) = 1903; selling price 1903 × (1 + 20%) = 76.
14. A. 136 m
Total distance 140 × 20 + 120 × 5 over 20 + 5 minutes: 136 m a minute.
15. 120 km
Let it be d km: d30 + d60 = 6, so d = 6 × 30 × 60 ÷ (30 + 60) = 120. Check: 4 + 2 = 6.
16. 18, 27
$32 is 48 below the average and $112 32 above, so the weights are 32 : 48 = 2 : 3. 45 kg in 2 : 3: 18 kg and 27 kg.
17. 4.8, 64, 75
Total distance 2 × 2.4 = 4.8 km = 4.8 × 1000 m, total time 36 + 28 = 64 minutes: 75 m a minute.
18. 37.2 dollars
Total cost ÷ total weight: (36 × 20 + 38 × 30) ÷ (20 + 30) = 37.2. Not (36 + 38) ÷ 2.

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