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 120120 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 120 by 2 gives 60.

  3. State the answer with its units

    60 km/h60\text{ km/h}

    The speed is 60 km/h.

Answer
60 km/h60\text{ km/h}
Question 2
1 markeasy
A runner covers 350350 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 350 by 50 gives 7.

  3. State the answer with its units

    7 m/s7\text{ m/s}

    The speed is 7 m/s.

Answer
7 m/s7\text{ m/s}
Question 3
1 markeasy
A cyclist rides at a steady 1515 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 15 by 3 gives 45.

  3. State the answer with its units

    45 km45\text{ km}

    The distance is 45 km.

Answer
45 km45\text{ km}
Question 4
1 markeasy
A train travels 210210 km at an average speed of 7070 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 210 by 70 gives 3.

  3. State the answer with its units

    3 hours3\text{ hours}

    The time is 3 hours.

Answer
3 hours3\text{ hours}
Question 5
1 markeasy
A metal block has mass 300300 g and volume 6060 cm3^3. Work out its density in g/cm3^3.

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 300 by 60 gives 5.

  3. State the answer with its units

    5 g/cm35\text{ g/cm}^3

    The density is 5 g per cubic centimetre.

Answer
5 g/cm35\text{ g/cm}^3

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