Key ideas
- Units: speed in km/h means kilometres travelled in 1 hour. Match your units: km and hours give km/h, miles and hours give mph, metres and seconds give m/s.
- Time intervals: count on. Go to the next whole hour, then whole hours, then the minutes left.
- Hours → minutes: × 60. So 0.4 h = 0.4 × 60 = 24 min.
- Minutes → hours: ÷ 60. So 15 min = 15 ÷ 60 = 0.25 h.
- Use the triangle. Cover the one you want with your finger and read off the formula: S = D ÷ T, D = S × T, T = D ÷ S.
- Write the formula, substitute (that's the first mark), then work it out and give the units.
- Times like 2 h 30 min must be changed to hours (2.5 h) before you use them. A time answer like 3.5 h can be changed back to 3 h 30 min.
Units
A train travels at 120 km/h. What does this mean? How far does it travel in 2 hours?(1 mark)
Read the units.120 km/h = 120 km in 1 hour
In plain EnglishThe "/h" means "per hour". So in every hour the train covers 120 kilometres.
Two hours.2 × 120 = 240 km✓1
In plain EnglishTwo hours means twice as far.
Time intervals
A bus leaves at 09:45 and arrives at 13:20. How long is the journey?(2 marks)
Count on to the next hour.09:45 → 10:00 = 15 min
In plain EnglishFrom quarter to ten up to ten o'clock is 15 minutes.
Whole hours, then the minutes left.10:00 → 13:00 = 3 h✓113:00 → 13:20 = 20 min
In plain EnglishJump in whole hours, then add the minutes at the end.
Add the jumps.15 min + 3 h + 20 min = 3 h 35 min✓2
In plain EnglishAdd the hours and the minutes.
Decimal time
Change 2.4 hours into hours and minutes.(2 marks)
Keep the whole hours.2.4 h = 2 h + 0.4 h
In plain EnglishThe 2 is two whole hours. Only the decimal part needs changing.
Decimal part × 60.0.4 × 60 = 24 min✓12.4 h = 2 h 24 min✓2
In plain EnglishThere are 60 minutes in an hour, so multiply by 60.
⚠ 2.4 h is not 2 h 40 min. The decimal is a part of an hour, not a number of minutes.
Write 1 hour 15 minutes in hours, as a decimal.(2 marks)
Minutes ÷ 60.15 ÷ 60 = 0.25 h✓1
In plain EnglishTo change minutes into hours, divide by 60.
Add the whole hours.1 h 15 min = 1.25 h✓2
In plain EnglishOne hour plus a quarter of an hour.
Speed, distance and time
A car travels 240 km in 3 hours. Calculate its average speed.(2 marks)
Use the triangle.
S = D ÷ T
In plain EnglishCover S with your finger. D is over T, so speed = distance ÷ time.
Substitute.S = D ÷ TS = 240 ÷ 3✓1
In plain EnglishWrite the formula, then put the numbers in. Substituting is the first mark.
Calculate, with units.S = 80 km/h✓2
In plain EnglishKilometres and hours give km/h.
A coach travels at 65 mph for 4 hours. How far does it travel?(2 marks)
Use the triangle.
D = S × T
In plain EnglishCover D. S and T are side by side, so multiply.
Substitute.D = S × TD = 65 × 4✓1
In plain EnglishPut in the speed and the time.
Calculate, with units.D = 260 miles✓2
In plain Englishmph means miles per hour, so the distance is in miles.
A cyclist travels 36 km at 12 km/h. How long does the journey take?(2 marks)
Use the triangle.
T = D ÷ S
In plain EnglishCover T. D is over S, so time = distance ÷ speed.
Substitute.T = D ÷ ST = 36 ÷ 12✓1
In plain EnglishDistance first, then divide by the speed.
Calculate, with units.T = 3 hours✓2
In plain Englishkm and km/h give a time in hours.
Using decimal time
A car travels 150 km in 2 hours 30 minutes. Calculate its average speed.(3 marks)
Change the time to hours.30 ÷ 60 = 0.5T = 2.5 h✓1
In plain EnglishThe formula needs the time in hours. 30 minutes is half an hour.
Substitute.S = D ÷ TS = 150 ÷ 2.5✓2
In plain EnglishCover S on the triangle: D ÷ T.
Calculate, with units.S = 60 km/h✓3
In plain EnglishCheck: 60 km/h for 2½ hours is 150 km. ✓
⚠ Don't type 2.30 into your calculator. 2 h 30 min is 2.5 hours, not 2.3.
A lorry travels 210 km at 60 km/h. How long does the journey take? Give your answer in hours and minutes.(3 marks)
Substitute.T = D ÷ ST = 210 ÷ 60✓1
In plain EnglishCover T: distance ÷ speed.
Calculate.T = 3.5 h✓2
In plain EnglishThis is in hours, as a decimal.
Change to hours and minutes.0.5 × 60 = 30 minT = 3 h 30 min✓3
In plain EnglishKeep the 3 whole hours and change the 0.5 into minutes: × 60.
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Your turn
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