Speed is distance divided by time, so speed = distance / time, distance = speed × time and time = distance / speed. The marks are almost never lost on the rearranging. They are lost on units: if the speed is in km/h then the time must be in hours, not minutes. To turn km/h into m/s multiply by 5/18, and to turn m/s into km/h multiply by 18/5.
Almost nobody gets the formula itself wrong. What goes wrong is mixing units inside one calculation. A question gives a speed in km/h and a time in minutes, the student divides straight away, and the answer is out by a factor of 60 with no working to save it.
The second issue is rearranging under pressure. Students who have only memorised speed = distance / time freeze when asked for the time. The fix is to write the formula down every single time and rearrange it on paper rather than trying to recall three separate versions.
Speed
speed = distance / time
Distance
distance = speed × time
Time
time = distance / speed
km/h to m/s
multiply by 5/18
m/s to km/h
multiply by 18/5
Minutes to hours
divide by 60
The three formulas are one formula rearranged, not three things to memorise. If you can only remember speed = distance / time, you can always recover the other two by treating it as an equation and changing the subject of the formula.
A cyclist travels 18 km at an average speed of 24 km/h. How long does the journey take, in minutes?
Solution
time = distance / speed.time = 18 / 24 = 0.75 hours.0.75 × 60 = 45 minutes.Quick check: 0.75 hours is three quarters of an hour, and three quarters of 60 is 45. If a decimal answer in hours looks odd, convert it to minutes and see whether it sounds like a sensible journey. A cyclist covering 18 km in 45 minutes is believable; 18 km in 45 seconds is not.
A train travels at 72 km/h. Find its speed in m/s, then find how far it travels in 25 seconds.
Solution
72 × 5/18 = 20 m/s.1000/3600 = 5/18.distance = speed × time = 20 × 25 = 500 m.The step students get wrong
Converting at the wrong moment. Students often convert the final answer instead of converting the speed at the start, which works only sometimes and fails whenever the calculation mixes two different units partway through. Convert first so that every number in the calculation is in the same system, then calculate once.
A car travels 60 km at 40 km/h, then 90 km at 60 km/h. Find the total time taken.
Solution
time = 60 / 40 = 1.5 hours.time = 90 / 60 = 1.5 hours.= 1.5 + 1.5 = 3 hours.Speeds do not add the same way. If that same question had asked for the average speed over the whole journey, you could not average 40 and 60 to get 50. That shortcut is the single most common error in this topic, and it has its own guide: the average speed mistake almost every student makes.
Why is the conversion factor 5/18?
Because 1 km/h means 1000 metres in 3600 seconds. 1000/3600 simplifies to 5/18. Going the other way, from m/s to km/h, you invert it and multiply by 18/5, which is the same as 3.6.
Do I have to convert to m/s every time?
No. Convert only when the units in the question do not already agree. If everything is in kilometres and hours, work in kilometres and hours. Converting when you did not need to is a common source of arithmetic slips.
What is the formula triangle and should I use it?
It is a triangle with distance on top and speed and time underneath, so covering the quantity you want shows you the operation. It works, but it only works for this one formula. Learning to rearrange properly is more useful because the same skill applies everywhere else in the paper.
How do I handle a speed given in minutes?
Convert the time to hours by dividing by 60 before you divide, or keep the whole calculation in minutes and state the speed per minute. Either is fine as long as you are consistent and you label the unit in the final answer.
How does this connect to the rest of E-Maths?
Speed is the most common context for direct and inverse proportion, since distance is proportional to time at constant speed. It is also the quantity you read off the axes in distance-time and speed-time graphs.
— Mr Gan Math Tuition
Mr. Gan drills the unit conversions until they stop costing marks in the paper.
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