Money, Exchange Rates, Time and Speed
These are the “real-life” number questions, and they are unusual in the syllabus: the mathematics is simple, but almost every mark lost comes from units — especially converting minutes into hours.
1. Speed, distance and time
Speed = Distance ÷ Time Distance = Speed × Time Time = Distance ÷ Speed
The triangle: cover the one you want, and the other two show what to do — D on top, S and T below.
The units must match the speed. For an answer in km/h, distance must be in km and time in hours. This single rule accounts for most errors in the topic.
Converting time — the biggest trap
Minutes to hours: DIVIDE by 60. 30 minutes = 0.5 hours. 45 minutes = 0.75 hours.
Never write 1 hour 30 minutes as 1.30 hours. It is 1.5 hours. Decimal hours are not the same as hours-and-minutes, and treating them as interchangeable is the classic error.
Converting back: 0.25 hours = 0.25 × 60 = 15 minutes. For 2.4 hours: 0.4 × 60 = 24, so 2 hours 24 minutes.
Other conversions:
- 1 hour = 3600 seconds
- Seconds to hours: divide by 3600. Multiplying instead was a recorded error
- m/s to km/h: × 3.6
Example: a car travels 150 km in 2 hours 30 minutes.
- Time = 2.5 hours
- Speed = 150 ÷ 2.5 = 60 km/h
2. Average speed
Average speed = TOTAL distance ÷ TOTAL time
You cannot average the speeds. If a journey is 60 km/h for one part and 40 km/h for another, the average is not 50 km/h unless the times are equal. Work out the total distance and the total time, then divide.
Example: 100 km at 50 km/h, then 120 km at 60 km/h.
- Time 1 = 100/50 = 2 h; Time 2 = 120/60 = 2 h
- Total distance = 220 km; total time = 4 h
- Average speed = 55 km/h
Divide, don’t subtract or multiply. Both errors were recorded — always return to the formula.
Include stops. If a journey has a 20-minute break, that time still counts in the total time for average speed.
3. Travel graphs
Distance–time graphs:
- Gradient = speed
- A horizontal line means stationary
- A steeper line means faster
- A line returning to zero means travelling back to the start
Speed–time graphs:
- Gradient = acceleration (negative = deceleration)
- Horizontal line = constant speed
- Area under the graph = distance travelled
These two graphs are not interchangeable. A horizontal line means stopped on a distance–time graph but constant speed on a speed–time graph. Confusing them was recorded, and it inverts the whole interpretation — check the y-axis label first.
Area under a speed–time graph gives distance. Split it into triangles and trapezia.
4. Time and timetables
The 24-hour clock:
- 09:30 = 9:30 am
- 14:45 = 2:45 pm
- 00:15 = 12:15 am
Don’t write “am” or “pm” with 24-hour times — the format already says it.
Calculating a duration: count up in stages rather than subtracting like decimals.
From 09:45 to 13:20:
- 09:45 → 10:00 is 15 min
- 10:00 → 13:00 is 3 hours
- 13:00 → 13:20 is 20 min
- Total = 3 hours 35 minutes
Time is base 60, not base 10. Subtracting 09:45 from 13:20 as if they were decimals gives the wrong answer — 13.20 − 9.45 = 3.75, which is not 3 h 35 min.
Timetables: read down a column for one vehicle’s journey, and across a row for one stop.
Time zones: add or subtract the difference, and watch for the date changing.
5. Money and exchange rates
Currency conversion is proportion.
Multiply to go one way, divide to come back.
Example: 1 GBP = 1.25 USD.
- £200 → 200 × 1.25 = $250
- $500 → 500 ÷ 1.25 = £400
Check the direction before you calculate. A sanity check: if the rate is above 1, converting to that currency should give a bigger number.
The exchange rate will be given in the exam — this was confirmed in lessons — so the marks are for using it in the right direction.
Money answers are normally given to 2 decimal places. Watch for questions asking for the nearest whole unit.
Other money contexts: wages (hourly rate × hours, plus overtime), profit and loss, bills with a fixed charge plus a rate per unit, and best-value comparisons using price per unit.
A fixed charge is added once, not per unit. For a bill of “£15 plus 8p per unit”, 200 units cost 15 + 0.08 × 200 = £31.
6. Mistakes that cost marks
Writing 1 h 30 min as 1.30 hours instead of 1.5.
Not converting minutes to hours before using a speed formula.
Dividing by 3600 when you should multiply, or vice versa.
Averaging speeds instead of using total distance ÷ total time.
Forgetting to include stops in the total time.
Mixing distance–time and speed–time graphs.
Subtracting times as decimals.
Writing “pm” with a 24-hour time.
Converting currency the wrong way.
Multiplying a fixed charge by the number of units.
Omitting units.
Frequently asked questions
What is the formula for speed? Speed = distance ÷ time.
How do I convert minutes to hours? Divide by 60 — 45 minutes is 0.75 hours.
Is 1 hour 30 minutes the same as 1.30 hours? No — it is 1.5 hours.
How do I find average speed? Total distance ÷ total time — including any stops.
Can I average two speeds? Only if the times are equal. Otherwise use the totals.
What does the gradient of a distance–time graph show? Speed. On a speed–time graph it shows acceleration.
What does the area under a speed–time graph show? Distance travelled.
What does a horizontal line mean? Stationary on a distance–time graph; constant speed on a speed–time graph.
How do I convert currency? Multiply by the exchange rate one way, divide the other. Check the direction.
How do I work out a duration? Count up in stages — time is base 60, not base 10.
Quick revision checklist
- I know the speed–distance–time triangle
- I convert minutes to hours by dividing by 60
- I never write 1 h 30 min as 1.30 hours
- I match my units to the speed units
- I use total distance ÷ total time for average speed
- I include stops in the total time
- I check the y-axis to tell the two travel graphs apart
- I know gradient = speed, and area = distance
- I can read the 24-hour clock and timetables
- I calculate durations by counting up in stages
- I can convert currency in both directions
- I handle fixed charges correctly
- I give money to 2 d.p. and always state units
These notes cover money, exchange rates, time and speed in the Cambridge IGCSE Mathematics (0580) syllabus, and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Maths lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.
Finished this topic?
Saved on this device — no account needed.