IGCSE Maths / Direct and inverse proportion
Speed, distance and time revision notes
Edexcel International GCSE Maths (4MA1), chapter 21: Direct and inverse proportion, specification point 4.4f. Free lesson.
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Average speed links distance and time through S = D/T, which can be rearranged to find either distance or time. Correct time and distance units matter because they determine the unit of the answer.
How speed, distance and time are linked
The formula for average speed is distance divided by time. Average speed is used because an object may not travel at one steady speed for the whole journey. Rearrange the formula when you need to find distance or time instead. S = D/T Rearrange for distance: D = S × T. Rearrange for time: T = D/S.
How the units determine your answer
The units for distance and time decide the unit for speed. Use matching units in the calculation: kilometres with hours gives km/h, while metres with seconds gives m/s. Convert the values before using the formula if the question asks for a different unit. Distance can be in kilometres or metres. Time can be in hours or seconds. For km/h, divide kilometres by hours. For m/s, divide metres by seconds.
How to convert km/h into m/s
Convert the distance unit first, then the time unit. Since 1 km = 1000 m and 1 h = 3600 s, converting km/h into m/s is the same as dividing by 3.6. To convert back, multiply by 3.6.
How to turn minutes into decimal hours
Minutes are counted out of 60, not out of 100. Divide the number of minutes by 60 to find the decimal part of an hour, then add it to the hours. This gives a time you can use with distance in kilometres to find speed in km/h. 30 min = 0.5 h, so 2 h 30 min = 2.5 h. 45 min = 0.75 h. 20 min = 0.333 h to three decimal places.
How to find average speed
Put the distance and time into S = D/T after expressing them in suitable units. Check that the resulting speed unit matches what the question asks for.