Rates practice questions

Rates questions

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1. 1RatesFoundation

   A car travels 180 miles in 3 hours at a constant rate. Enter its speed in miles per hour.A car travels 180 miles in 3 hours at a constant rate. Enter its speed in miles per hour.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 6060

   Rate equals distance divided by time: 1803 = 60 miles per hour.Rate equals distance divided by time: 180/3 = 60 miles per hour.

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2. 2RatesFoundation

   A printer produces 45 pages in 3 minutes at a constant rate. Enter the number of pages it produces in 8 minutes.A printer produces 45 pages in 3 minutes at a constant rate. Enter the number of pages it produces in 8 minutes.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 120120

   The rate is 453 = 15 pages per minute, and 15 × 8 = 120 pages.The rate is 45/3 = 15 pages per minute, and 15 × 8 = 120 pages.

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3. 3RatesStandard

   A pump moves 4,200 liters in 3.5 hours. Enter its rate in liters per hour.A pump moves 4,200 liters in 3.5 hours. Enter its rate in liters per hour.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 12001200

   Divide the volume by the time: 42003.5 = 1200 liters per hour.Divide the volume by the time: 4200/3.5 = 1200 liters per hour.

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4. 4RatesStandard

   A train travels 210 kilometers in 2 hours 30 minutes. Enter its average speed in kilometers per hour.A train travels 210 kilometers in 2 hours 30 minutes. Enter its average speed in kilometers per hour.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 8484

   Convert the time to hours first: 2 hours 30 minutes is 2.5 hours. Then 2102.5 = 84 kilometers per hour.Convert the time to hours first: 2 hours 30 minutes is 2.5 hours. Then 210/2.5 = 84 kilometers per hour.

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5. 5RatesStandard

   A printer produces 14 pages a minute. How many minutes does it take to print 630 pages?A printer produces 14 pages a minute. How many minutes does it take to print 630 pages?

   • A3535
   • B4545
   • C5050
   • D4444
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   Answer: 4545

   Dividing the total by the rate gives 63014 = 45 minutes. Multiplying instead of dividing, or dividing by the wrong figure, produces the other choices.Dividing the total by the rate gives 630/14 = 45 minutes. Multiplying instead of dividing, or dividing by the wrong figure, produces the other choices.

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6. 6RatesStandard

   A tap fills a 240-liter tank in 16 minutes. Enter the number of liters it delivers per minute.A tap fills a 240-liter tank in 16 minutes. Enter the number of liters it delivers per minute.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 1515

   Dividing the volume by the time gives 24016 = 15 liters a minute.Dividing the volume by the time gives 240/16 = 15 liters a minute.

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7. 7RatesStandard

   A cyclist covers 54 km in 2 hours and 15 minutes. What is the average speed in kilometers per hour?A cyclist covers 54 km in 2 hours and 15 minutes. What is the average speed in kilometers per hour?

   • A2727
   • B21.621.6
   • C2424
   • D3636
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   Answer: 2424

   2 hours 15 minutes is 2.25 hours, and 542.25 = 24 km/h. Dividing by 2 instead gives 27, which treats the extra quarter-hour as free.2 hours 15 minutes is 2.25 hours, and 54/2.25 = 24 km/h. Dividing by 2 instead gives 27, which treats the extra quarter-hour as free.

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8. 8RatesStandard

   A train covers 45 km in 36 minutes. What is its average speed in kilometers per hour?A train covers 45 km in 36 minutes. What is its average speed in kilometers per hour?

   • A6060
   • B7575
   • C8080
   • D5454
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   Answer: 7575

   36 minutes is 0.6 hours, and 450.6 = 75 km/h. Dividing by 36 rather than converting to hours first gives a figure per minute, not per hour.36 minutes is 0.6 hours, and 45/0.6 = 75 km/h. Dividing by 36 rather than converting to hours first gives a figure per minute, not per hour.

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9. 9RatesStandard

   A coach covers 84 km in 1 hour and 12 minutes. What is its average speed in kilometers per hour?A coach covers 84 km in 1 hour and 12 minutes. What is its average speed in kilometers per hour?

   • A6262
   • B7575
   • C8484
   • D7070
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   Answer: 7070

   1 hour 12 minutes is 1.2 hours, and 841.2 = 70 km/h. Treating the 12 minutes as 0.12 of an hour gives about 75, which is the commonest conversion slip.1 hour 12 minutes is 1.2 hours, and 84/1.2 = 70 km/h. Treating the 12 minutes as 0.12 of an hour gives about 75, which is the commonest conversion slip.

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10. 10RatesChallenge

    One tap fills a tank in 6 minutes and a second tap fills the same tank in 12 minutes. Enter the number of minutes the two taps take to fill it together.One tap fills a tank in 6 minutes and a second tap fills the same tank in 12 minutes. Enter the number of minutes the two taps take to fill it together.

    Student-produced response: write your own answer rather than choosing one.

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    Answer: 44

    In one minute the taps fill 16 and 112 of the tank, so together they fill 16 + 112 = 312 = 14 of the tank per minute. Filling the whole tank takes 4 minutes.In one minute the taps fill 1/6 and 1/12 of the tank, so together they fill 1/6 + 1/12 = 3/12 = 1/4 of the tank per minute. Filling the whole tank takes 4 minutes.

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11. 11RatesChallenge

    A cyclist rides 12 kilometers at 24 km/h and then 12 kilometers at 12 km/h. What is the average speed for the whole ride?A cyclist rides 12 kilometers at 24 km/h and then 12 kilometers at 12 km/h. What is the average speed for the whole ride?

    • A20 km/h20 km/h
    • B16 km/h16 km/h
    • C15 km/h15 km/h
    • D18 km/h18 km/h
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    Answer: 16 km/h16 km/h

    Average speed is total distance over total time, not the average of the speeds. The legs take 0.5 and 1 hour, so 24 kilometers in 1.5 hours gives 16 km/h. The tempting 18 km/h is the average of the two speeds.Average speed is total distance over total time, not the average of the speeds. The legs take 0.5 and 1 hour, so 24 kilometers in 1.5 hours gives 16 km/h. The tempting 18 km/h is the average of the two speeds.

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12. 12RatesChallenge

    A cyclist covers 45 kilometers at 15 km/h and returns along the same road at 30 km/h. Enter the average speed for the whole journey in km/h.A cyclist covers 45 kilometers at 15 km/h and returns along the same road at 30 km/h. Enter the average speed for the whole journey in km/h.

    Student-produced response: write your own answer rather than choosing one.

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    Answer: 2020

    Average speed is total distance over total time. The legs take 3 hours and 1.5 hours, so 90 kilometers in 4.5 hours gives 20 km/h. Averaging the two speeds would give 22.5, which is wrong because more time is spent at the slower speed.Average speed is total distance over total time. The legs take 3 hours and 1.5 hours, so 90 kilometers in 4.5 hours gives 20 km/h. Averaging the two speeds would give 22.5, which is wrong because more time is spent at the slower speed.

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13. 13RatesChallenge

    A driver covers 60 km at 60 km/h and the next 60 km at 40 km/h. What is the average speed for the whole journey?A driver covers 60 km at 60 km/h and the next 60 km at 40 km/h. What is the average speed for the whole journey?

    • A50 km/h50 km/h
    • B52 km/h52 km/h
    • C48 km/h48 km/h
    • D45 km/h45 km/h
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    Answer: 48 km/h48 km/h

    Average speed is total distance over total time. The two legs take 1 hour and 1.5 hours, so 120 km in 2.5 hours is 48 km/h. Averaging the two speeds gives 50, which would only be right if equal time were spent at each.Average speed is total distance over total time. The two legs take 1 hour and 1.5 hours, so 120 km in 2.5 hours is 48 km/h. Averaging the two speeds gives 50, which would only be right if equal time were spent at each.

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