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PSLE Mathematics · Primary 5 and 6

Speed

Speed tells you how far something travels in one unit of time. In Primary 6 you calculate speed, distance and time, convert between units such as km/h and m/s, and find the average speed for a whole journey. Speed questions combine fractions, decimals and time, so they test several skills at once. This guide sets out the three formulas, the unit conversions you need, the average speed trap and a way to handle journeys with two people, followed by a worked example and practice.

What the syllabus expects

  • Understand speed as the distance travelled per unit of time, in units such as km/h, m/min and m/s
  • Calculate speed, distance or time when the other two are given
  • Convert between units of time and between units of speed
  • Find average speed as total distance divided by total time
  • Solve word problems involving speed, including journeys with more than one part

Speed, distance and time

Speed is the distance travelled in one unit of time. A car moving at 60 km/h covers 60 km in each hour. Three formulas connect the quantities: speed = distance ÷ time, distance = speed × time, and time = distance ÷ speed. For example, a train that travels 150 km in 2 h has a speed of 150 ÷ 2 = 75 km/h. A cyclist riding at 18 km/h for 3 h covers 18 × 3 = 54 km. A runner covering 400 m at 5 m/s takes 400 ÷ 5 = 80 s. The units must match. If speed is in km/h, distance must be in km and time in hours. A quick check is to read the unit of the answer: km ÷ h gives km/h, which is a speed.

Converting units of time and speed

Minutes must usually be changed into hours as a fraction or a decimal. 30 min = 1/2 h, 15 min = 1/4 h, 45 min = 3/4 h, 20 min = 1/3 h and 2 h 30 min = 2.5 h, not 2.3 h. To convert km/h into m/min, change the kilometres into metres and the hours into minutes: 60 km/h = 60 000 m in 60 min = 1000 m/min. To convert km/h into m/s, use 1 h = 3600 s: 18 km/h = 18 000 m in 3600 s = 5 m/s. Going the other way, 10 m/s = 10 × 3600 = 36 000 m in 1 h = 36 km/h. When you find a duration from clock times, count in steps: from 10.40 a.m. to 12.40 p.m. is 2 h, and on to 1.15 p.m. is another 35 min, giving 2 h 35 min.

Average speed

Average speed = total distance ÷ total time. It is not the average of the speeds. Suppose a van travels 60 km at 60 km/h and then another 60 km at 40 km/h. The first part takes 60 ÷ 60 = 1 h and the second part takes 60 ÷ 40 = 1.5 h. The total distance is 120 km and the total time is 2.5 h, so the average speed is 120 ÷ 2.5 = 48 km/h, not (60 + 40) ÷ 2 = 50 km/h. The van spends longer at the slower speed, which pulls the average down. If the question asks for the average speed for the whole journey and the driver stops for a rest, the rest time counts in the total time.

Journeys with two people

When two people move at the same time, think about what happens in each hour. If two cars start at the same time from towns 210 km apart and drive towards each other at 60 km/h and 80 km/h, the distance between them shrinks by 60 + 80 = 140 km every hour. They meet after 210 ÷ 140 = 1.5 h. Check: 60 × 1.5 = 90 km and 80 × 1.5 = 120 km, which add up to 210 km. If one person chases another along the same route, the gap shrinks by the difference in their speeds each hour. A line diagram with the starting points, times and distances marked keeps the information organised, and a table of time against distance for each person works well when they start at different times.

Worked example

Mr Lee drove from Town A to Town B at an average speed of 72 km/h. He left Town A at 9.15 a.m. and arrived at Town B at 11.45 a.m. He drove back along the same road at an average speed of 90 km/h. (a) What is the distance between the two towns? (b) What was his average speed for the whole return trip, there and back?

  1. Time from 9.15 a.m. to 11.45 a.m. is 2 h 30 min = 2.5 h.
  2. Distance = speed × time = 72 × 2.5 = 180 km.
  3. Time for the return journey = distance ÷ speed = 180 ÷ 90 = 2 h.
  4. Total distance there and back = 180 + 180 = 360 km.
  5. Total time = 2.5 + 2 = 4.5 h.
  6. Average speed = total distance ÷ total time = 360 ÷ 4.5 = 80 km/h.
  7. Check: averaging the two speeds would give 81 km/h, which is wrong because he spent more time at the slower speed, so the true average must be below 81 km/h.

Answer: (a) 180 km (b) 80 km/h

Common mistakes

  • Averaging the speeds instead of using total distance ÷ total time. In the worked example, (72 + 90) ÷ 2 = 81 km/h is wrong, and the correct answer is 80 km/h.
  • Writing 2 h 30 min as 2.3 h. There are 60 minutes in an hour, so 30 min = 0.5 h and the time is 2.5 h.
  • Mixing units, such as dividing a distance in metres by a time in hours. Convert first so that the units match the speed you want.
  • Leaving out a rest stop when the question asks for average speed over the whole journey. The time spent resting counts in the total time.
  • Counting time intervals wrongly across noon. 10.40 a.m. to 1.15 p.m. is 2 h 35 min, so count to the next whole hour in steps instead of subtracting the clock numbers.
  • Using the wrong formula, such as time = speed ÷ distance. Check that the unit of your answer makes sense, because km ÷ km/h gives hours.

Exam tips

  • Write times in hours as fractions where possible, such as 15 min = 1/4 h, because fractions often cancel neatly with speeds like 72 km/h.
  • Draw a line diagram for any journey with more than one part, and mark each part's distance, time and speed before calculating.
  • Write the formula in words before you substitute, for example 'average speed = total distance ÷ total time', so you do not average the speeds by habit.

Practice questions

1. Easy: A cyclist travels 36 km in 2 h 15 min. Find his average speed in km/h.

Show answer

16 km/h. Working: 2 h 15 min = 2 1/4 h = 2.25 h, and 36 ÷ 2.25 = 16 km/h.

2. Medium: Express a speed of 54 km/h in m/s.

Show answer

15 m/s. Working: 54 km = 54 000 m and 1 h = 3600 s, so 54 000 ÷ 3600 = 15 m/s.

3. Harder: Lina left her home at 8.00 a.m. and walked to the library at 4 km/h. Her brother left home at 8.30 a.m. and cycled along the same route at 12 km/h. At what time did he catch up with her?

Show answer

8.45 a.m. Working: by 8.30 a.m. Lina had walked 4 × 1/2 = 2 km. The brother closes the gap by 12 − 4 = 8 km each hour, so he needs 2 ÷ 8 = 1/4 h = 15 min. Check: at 8.45 a.m. Lina has walked 4 × 3/4 = 3 km and her brother has cycled 12 × 1/4 = 3 km.

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