Average speed questions with answers

Questions

1. Question 1Distances and times given

   A motorcyclist travels from A to B and then from B to C, as shown in the diagram. The journey from A to B takes 1.5 hours and the journey from B to C takes 0.5 hours. Find the average speed for the whole journey, in km/h.

   Show the worked solution

   1. Step 1: Total distance$\text{Total distance} = 45 + 25$$\phantom{\text{Total distance}} = 70 \text{ km}$
   2. Step 2: Total time$\text{Total time} = 1.5 + 0.5$$\phantom{\text{Total time}} = 2 \text{ h}$
   3. Step 3: Average speed = total distance ÷ total time$\text{Average speed} = \dfrac{70}{2}$$\phantom{\text{Average speed}} = 35 \text{ km/h}$
2. Question 2Speeds and times: find each distance

   A car travels for 1.5 hours at an average speed of 90 km/h, and then for 3 hours at an average speed of 30 km/h. Find the average speed, in km/h, for the whole journey.

   Show the worked solution

   1. Step 1: Find each distance: speed × time$90 \times 1.5 = 135 \text{ km}$$30 \times 3 = 90 \text{ km}$
   2. Step 2: Total distance$\text{Total distance} = 135 + 90$$\phantom{\text{Total distance}} = 225 \text{ km}$
   3. Step 3: Total time$\text{Total time} = 1.5 + 3$$\phantom{\text{Total time}} = 4.5 \text{ h}$
   4. Step 4: Average speed = total distance ÷ total time$\text{Average speed} = \dfrac{225}{4.5}$$\phantom{\text{Average speed}} = 50 \text{ km/h}$
3. Question 3Distances and speeds: find each time

   A bus travels from A to B at an average speed of 75 km/h and then from B to C at an average speed of 20 km/h. The distances are shown in the diagram. Find the average speed, in km/h, for the whole journey.

   Show the worked solution

   1. Step 1: Find each time: distance ÷ speed$\dfrac{150}{75} = 2 \text{ h}$$\dfrac{60}{20} = 3 \text{ h}$
   2. Step 2: Total distance$\text{Total distance} = 150 + 60$$\phantom{\text{Total distance}} = 210 \text{ km}$
   3. Step 3: Total time$\text{Total time} = 2 + 3$$\phantom{\text{Total time}} = 5 \text{ h}$
   4. Step 4: Average speed = total distance ÷ total time$\text{Average speed} = \dfrac{210}{5}$$\phantom{\text{Average speed}} = 42 \text{ km/h}$
4. Question 4Times in minutes

   A motorcyclist travels from A to B in 50 minutes and then from B to C in 40 minutes. The distances are shown in the diagram. Find the average speed for the whole journey, in km/h.

   Show the worked solution

   1. Step 1: Total distance$\text{Total distance} = 30 + 15$$\phantom{\text{Total distance}} = 45 \text{ km}$
   2. Step 2: Total time, in hours (minutes ÷ 60)$\text{Total time} = \dfrac{50 + 40}{60}$$\phantom{\text{Total time}} = 1.5 \text{ h}$
   3. Step 3: Average speed = total distance ÷ total time$\text{Average speed} = \dfrac{45}{1.5}$$\phantom{\text{Average speed}} = 30 \text{ km/h}$
5. Question 5Find the speed for the rest of the journey

   A bus travels 240 km from A to C through B. The average speed for the whole journey is 80 km/h. The 60 km from A to B takes 1 hour. Find the average speed from B to C.

   Show the worked solution

   1. Step 1: Total time = total distance ÷ average speed$\text{Total time} = \dfrac{240}{80}$$\phantom{\text{Total time}} = 3 \text{ h}$
   2. Step 2: Distance and time for B to C$\text{Distance} = 240 - 60$$\phantom{\text{Distance}} = 180 \text{ km}$$\text{Time} = 3 - 1$$\phantom{\text{Time}} = 2 \text{ h}$
   3. Step 3: Speed = distance ÷ time$\text{Speed} = \dfrac{180}{2}$$\phantom{\text{Speed}} = 90 \text{ km/h}$