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Mathematics › ⚡ Grade 6 › Speed Track: Distance, Time, and Constant Speed
⚡ Grade 6 · Lesson 2 of 14

Speed Track: Distance, Time, and Constant Speed

Moving at a steady speed means covering the same distance every hour — plot it and you get a straight line starting right at zero.

Grade 6Pre-Algebra
Speed Track: Distance, Time, and Constant Speed — illustration
💡
The big idea: Speed is a rate: it tells you how much distance is covered for every unit of time. When something moves at a constant speed, distance and time always match up the same way — double the time, double the distance — so distance = speed × time. Plotting distance against time gives a straight line that starts at (0, 0), because at time zero nothing has been traveled yet.
🎯 By the end, you'll be able to
  • Explain speed as a rate: distance covered per unit of time
  • Use distance = speed × time to find a distance, given a speed and a time
  • Recognise that constant speed graphs as a straight line through the start point (0, 0)
  • Compare two constant speeds by comparing how steep their distance-time lines are
📎 You should already know
  • Multiplication and division facts
  • Ratios and unit rates

Moving at a steady pace

Picture a go-kart on a speed track, cruising at a steady 40 kilometres per hour. Every hour it covers another 40 km: after 1 hour, 40 km; after 2 hours, 80 km; after 3 hours, 120 km. That “same amount every hour” is exactly what a rate means.

Speed is just a rate for distance: how much ground you cover for every unit of time that passes.

🔑 Speed is a rate: distance per time
Speed tells you how much distance is covered in one unit of time (one hour, one second, one minute). A constant speed means that rate never changes — the same distance is added for every equal chunk of time.
\[ \text{distance} = \text{speed} \times \text{time} \]
The key relationship for constant speed. Know any two of the three and you can find the third.

Finding distance, or finding the speed

If you know the speed and the time, multiply to get the distance. If instead you know the distance actually covered and the time it took, divide distance by time to find the unit rate — the speed. Either way, the same three quantities are connected by one relationship.

📝 Worked example: A car travels at a constant 50 km/h for 3 hours. How far does it go?
  1. Use distance = speed × time.
  2. Speed = 50 km/h, time = 3 h.
  3. Distance = 50 × 3.
✓ The car travels <strong>150 km</strong>.

Graphing constant speed

Plot distance on the vertical axis and time on the horizontal axis. At time 0, no time has passed, so the distance traveled is 0 too — the graph always starts at the point (0, 0). Because the speed never changes, the same distance is added every hour, and the graph is a perfectly straight line through that starting point.

🎮 Interactive: speed as the steepness of the line LIVE
Drag the Speed slider to make the line climb faster or slower; the graph reads distance against time, so a steeper line covers more distance every hour. Keep the start at 0 for a trip that begins at the start line.
✨ Steeper line, faster speed
Two vehicles that start together and both move at constant speed can be compared just by looking at their lines: the steeper line belongs to the faster one, because it covers more distance in the same amount of time.
📝 Worked example: A cyclist covers 40 km in 2 hours at a constant speed. What is the cyclist's speed?
  1. This time you know the distance and the time, so divide instead of multiply.
  2. Speed = distance ÷ time = 40 ÷ 2.
  3. That gives the distance covered in exactly 1 hour — the unit rate.
✓ The cyclist's speed is <strong>20 km/h</strong>.
📝 Worked example: Car A travels 60 miles in 1 hour; Car B travels 90 miles in 1 hour, both at constant speed. Which line is steeper on a distance-vs-time graph?
  1. Car A's speed is 60 mph; Car B's speed is 90 mph.
  2. A larger speed means more distance covered every hour, which makes the line climb faster.
  3. 90 > 60, so Car B's line climbs more per hour.
✓ <strong>Car B's</strong> line is steeper, matching its faster 90 mph speed.
⚠️ Divide the right way around
To find a speed from a distance and a time, always divide distance ÷ time, not time ÷ distance. Dividing the wrong way gives hours-per-kilometre instead of kilometres-per-hour — check that your answer's units make sense for a speed.

Check your understanding

1. A car travels at a constant 45 km/h. How far does it travel in 4 hours?
Distance = speed × time = 45 × 4 = 180 km.
2. A cyclist covers 60 km in 3 hours at a constant speed. What is the speed?
Speed = distance ÷ time = 60 ÷ 3 = 20 km/h.
3. On a distance-vs-time graph for someone moving at a constant speed, the line passes through…
At time 0, no distance has been traveled yet, so the graph always starts at the origin (0, 0).
4. Car P travels at a constant 70 mph, and Car Q at a constant 55 mph. Whose distance-time line is steeper?
A larger speed covers more distance every hour, giving a steeper line. Since 70 > 55, Car P's line is steeper.
5. A train travels 300 miles in 5 hours at a constant speed. How many miles does it cover in 1 hour?
Speed = distance ÷ time = 300 ÷ 5 = 60 miles per hour, so it covers 60 miles in 1 hour.
✅ Key takeaways
  • Speed is a rate: the distance covered per unit of time.
  • Constant speed means distance = speed × time, for any time you pick.
  • A distance-vs-time graph for constant speed is a straight line through the start point (0, 0).
  • The steeper the line, the faster the speed — compare speeds by comparing steepness.
  • To find a speed from a distance and a time, divide distance by time.