Compound measures Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Compound measures questions. See exactly how to solve problems on speed, distance divided by time, metres per second, distance = speed x time.

speeddistance divided by timemetres per seconddistance = speed x timetime = distance / speeddensity
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
A car travels 120 km120\,\mathrm{km} in 22 hours. Work out its average speed in km/h.

Worked solution

  1. Write down the formula

    speed=distancetime\text{speed} = \frac{\text{distance}}{\text{time}}

    Speed is the distance divided by the time.

  2. Substitute the values and divide

    speed=1202=60\text{speed} = \frac{120}{2} = 60

    Dividing 120120 by 22 gives 6060.

  3. State the answer with its units

    60 km/h60\,\mathrm{km/h}

    The speed is 60 km/h60\,\mathrm{km/h}.

Answer
60 km/h60\,\mathrm{km/h}
Question 2
1 markeasy
A runner covers 350 m350\,\mathrm{m} in 5050 seconds. Work out the average speed in m/s.

Worked solution

  1. Write down the formula

    speed=distancetime\text{speed} = \frac{\text{distance}}{\text{time}}

    Speed is the distance divided by the time.

  2. Substitute the values and divide

    speed=35050=7\text{speed} = \frac{350}{50} = 7

    Dividing 350350 by 5050 gives 77.

  3. State the answer with its units

    7 m/s7\,\mathrm{m/s}

    The speed is 7 m/s7\,\mathrm{m/s}.

Answer
7 m/s7\,\mathrm{m/s}
Question 3
1 markeasy
A cyclist rides at a steady 15 km/h15\,\mathrm{km/h} for 33 hours. Work out the distance travelled.

Worked solution

  1. Write down the formula

    distance=speed×time\text{distance} = \text{speed} \times \text{time}

    Rearranged, the formula gives the quantity as a product.

  2. Substitute the values and multiply

    15×3=4515 \times 3 = 45

    Multiplying 1515 by 33 gives 4545.

  3. State the answer with its units

    45 km45\,\mathrm{km}

    The distance is 45 km45\,\mathrm{km}.

Answer
45 km45\,\mathrm{km}
Question 4
1 markeasy
A train travels 210 km210\,\mathrm{km} at an average speed of 70 km/h70\,\mathrm{km/h}. Work out the time taken, in hours.

Worked solution

  1. Write down the formula

    time=distancespeed\text{time} = \frac{\text{distance}}{\text{speed}}

    Time is the distance divided by the speed.

  2. Substitute the values and divide

    time=21070=3\text{time} = \frac{210}{70} = 3

    Dividing 210210 by 7070 gives 33.

  3. State the answer with its units

    3 hours3\text{ hours}

    The time is 33 hours.

Answer
3 hours3\text{ hours}
Question 5
1 markeasy
A metal block has mass 300 g300\,\mathrm{g} and volume 60 cm360\,\mathrm{cm}^3. Work out its density in g/cm3\mathrm{g/cm}^3.

Worked solution

  1. Write down the formula

    density=massvolume\text{density} = \frac{\text{mass}}{\text{volume}}

    Density is the mass divided by the volume.

  2. Substitute the values and divide

    density=30060=5\text{density} = \frac{300}{60} = 5

    Dividing 300300 by 6060 gives 55.

  3. State the answer with its units

    5 g/cm35\,\mathrm{g/cm}^3

    The density is 5 g5\,\mathrm{g} per cubic centimetre.

Answer
5 g/cm35\,\mathrm{g/cm}^3

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