Speed, distance and time questions with answers

Questions

1. Question 1Find the speed

   A car travels 20 km in 0.5 hours at a constant speed. Find its speed in km/h.

   Show the worked solution

   1. Step 1: Find the speed: multiply or divide?$\text{Speed} = \dfrac{20}{0.5}$$= 40$The speed is $40$ km/h.
2. Question 2Find the distance (time in minutes)

   A car travels at a constant speed of 36 km/h for 36 minutes. Find the distance it travels, in km.

   Show the worked solution

   1. Step 1: Change the time to hours (minutes ÷ 60)$36 \text{ min} = \dfrac{36}{60} \text{ h}$$\phantom{36 \text{ min}} = 0.6 \text{ h}$
   2. Step 2: Find the distance: multiply or divide?$\text{Distance} = 36 \times 0.6$$= 21.6$The distance is $21.6$ km.
3. Question 3Find the time in hours and minutes

   A train travels 100 km at a constant speed of 40 km/h. Find the time taken. Give your answer in hours and minutes.

   Show the worked solution

   1. Step 1: Find the time in hours: multiply or divide?$\text{Time} = \dfrac{100}{40}$$= 2.5$
   2. Step 2: Change the decimal part of an hour into minutes (× 60)$0.5 \text{ h} = 0.5 \times 60 \text{ min}$$\phantom{0.5 \text{ h}} = 30 \text{ min}$Time taken $= 2$ h $30$ min
4. Question 4Change between km/h and m/s

   Express $90$ km/h in m/s.

   Show the worked solution

   1. Step 1: Change km to m and h to s$90 \text{ km/h} = \dfrac{90 \times 1000}{3600} \text{ m/s}$$\phantom{90 \text{ km/h}} = 25 \text{ m/s}$
5. Question 5Mixed units

   A skater moves at a constant speed of 4 m/s for 25 minutes. Find the distance covered, in km.

   Show the worked solution

   1. Step 1: Change the time to seconds (the speed is in m/s)$25 \text{ min} = 25 \times 60 \text{ s}$$\phantom{25 \text{ min}} = 1500 \text{ s}$
   2. Step 2: Find the distance in metres: multiply or divide?$\text{Distance} = 4 \times 1500$$= 6000$
   3. Step 3: Change metres to kilometres (÷ 1000)$\dfrac{6000}{1000} = 6 \text{ km}$
6. Question 6A train passing through a tunnel

   A train 240 m long travels at a constant speed of 72 km/h. It takes 57 seconds to pass completely through a tunnel, from the moment its front reaches the tunnel to the moment its back leaves it. Find the length of the tunnel, in metres.

   Show the worked solution

   1. Step 1: Change the speed to metres per second (÷ 3.6)$72 \text{ km/h} = \dfrac{72}{3.6}$$\phantom{72 \text{ km/h}} = 20 \text{ m/s}$
   2. Step 2: Distance = speed × time$\text{Distance} = 20 \times 57$$\phantom{\text{Distance}} = 1140 \text{ m}$
   3. Step 3: The back of the train must also clear the tunnel: the train travels the tunnel's length PLUS its own length: take the train's length away$\text{Length of the tunnel} = 1140 - 240$$\phantom{\text{Length of the tunnel}} = 900 \text{ m}$
7. Question 7Turns of a wheel per minute

   A bicycle travels at a constant speed of 27 km/h. Each of its wheels has a diameter of 66 cm and turns without slipping. Find the number of complete turns (revolutions) each wheel makes in one minute, correct to the nearest whole number.

   Show the worked solution

   1. Step 1: The distance travelled in one minute, in cm (1 km = 100 000 cm, 1 h = 60 min)$\dfrac{27 \times 100\,000}{60} = 45000 \text{ cm}$
   2. Step 2: One turn of the wheel covers its circumference: π × diameter$\pi \times 66 = 207.34\ldots \text{ cm}$
   3. Step 3: Turns in one minute: distance ÷ circumference$\text{Turns} = \dfrac{45000}{207.34\ldots}$$\phantom{\text{Turns}} = 217.02\ldots \approx 217$