About Time and Distance
Every time and distance question comes from a single relation: distance equals speed multiplied by time. The formula is never the difficulty. The difficulty is that the three quantities are handed to you in different units, and one of them has to be converted before anything can be calculated. Once the units agree, the question is a multiplication.
What you need to understand
- Distance = speed x time. Rearranged, that gives speed = distance / time and time = distance / speed.
- Units must agree before you substitute. Kilometres go with hours, metres go with seconds, and mixing the two is the single commonest mistake in the topic.
- One kilometre per hour is 5/18 of a metre per second, so converting into m/s always makes the number smaller.
- Speeds add when two bodies move towards each other and subtract when they move in the same direction.
- If the speed is multiplied by k, the time for the same journey is divided by k. Doubling the speed halves the time.
- The saving in time when a speed is raised is the slower time minus the faster time, and nothing else.
Formulas to remember
How to work through these questions
- Write the three quantities down as speed, distance and time, and mark which one the question is asking for.
- Decide the units at the very start and convert everything into that pair before doing any arithmetic.
- When a question mentions a change of speed, work out the two journey times separately and subtract them instead of looking for a shortcut.
- Check the size of your answer against a known speed. At 60 km/hr a car covers 60 km in an hour, so 600 km cannot be a two hour journey.
- For a conversion into m/s, remember that the answer must be smaller than the km/hr figure, because a metre per second is the faster unit.
Mistakes that cost marks
- Mixing kilometres with minutes, which throws the answer out by a factor of sixty.
- Multiplying by 18/5 when converting km/hr into m/s, so making the speed larger instead of smaller.
- Adding two speeds when the bodies travel in the same direction, where the relative speed is the difference.
- Reporting one of the two journey times when the question asked for the time saved.
- Leaving a time of 20 minutes as 20 when the speed is in km per hour.
Worked example
A car travels 288 km at a steady speed of 72 km/hr. How long does the journey take?
- The quantity asked for is time, so the rearrangement needed is time = distance / speed.
- Substitute: time = 288 / 72.
- Since 72 x 4 = 288, the journey takes 4 hours.
- Check: at 72 km/hr a car covers 72 km each hour, and over 4 hours that is 288 km, which matches the question.
Answer: 4 hours
Practice questions with answers
A few Time and Distance questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
A bus moves at 88 km per hour for 7 hours. How far does it travel?
Answer: Option C — with explanation
Distance = speed x time, with the time already given in hours.
Distance = 88 x 7 = 616 km.
Common mistakes
- used one extra hour in the multiplication: 704
- added the speed and the time instead of multiplying them: 95
- divided the speed by the time: 12.57
Question 2
A car is travelling at 252 km/hr. What is its speed in m/s?
-
A
907.2
-
B
1260
-
C
70
-
D
252
Answer: Option C — with explanation
Changing km/hr into m/s means multiplying by 1000/3600, which simplifies to 5/18.
Speed = 252 x \(\frac{5}{18}\) = 70 m/s.
Common mistakes
- multiplied by 5 instead of by 5/18: 1260
- left the speed in km/hr: 252
- inverted the conversion factor and multiplied by 18/5: 907.2
Question 3
A bus covers 320 km at 20 km/hr. How much time is saved if the speed is raised to 80 km/hr?
Answer: Option C — with explanation
The saving is the difference between the two journey times.
Original time = 320 / 20 = 16 hours; new time = 320 / 80 = 4 hours.
Time saved = 16 - 4 = 12 hours.
Common mistakes
- added the two journey times instead of subtracting them: 20
- reported the new journey time instead of the time saved: 4
- reported the original journey time instead of the time saved: 16
Question 4
A bus moves at 27 km per hour for 4 hours. How far does it travel?
Answer: Option D — with explanation
Distance = speed x time, with the time already given in hours.
Distance = 27 x 4 = 108 km.
Common mistakes
- reported the speed instead of the distance: 27
- divided the speed by the time: 6.75
- used one extra hour in the multiplication: 135
Question 5
A car travels 432 km at 27 km/hr. Find the reduction in journey time if it is driven at 108 km/hr instead.
Answer: Option B — with explanation
The saving is the difference between the two journey times.
Original time = 432 / 27 = 16 hours; new time = 432 / 108 = 4 hours.
Time saved = 16 - 4 = 12 hours.
Common mistakes
- reported the new journey time instead of the time saved: 4
- added the two journey times instead of subtracting them: 20
- reported the original journey time instead of the time saved: 16
Frequently asked questions
How do I convert a speed from km/hr into m/s?
Multiply by 5/18. A speed of 90 km/hr is 90 x 5/18 = 25 m/s. The number becomes smaller because a metre per second is a faster speed than a kilometre per hour.
What is the relative speed of two trains travelling in opposite directions?
Add the two speeds. If they travel in the same direction, subtract the smaller speed from the larger one, because the faster train is only gaining on the slower one.
Can I use the formula when the time is given in minutes?
Yes, but convert the minutes into hours first, or convert the speed into kilometres per minute. A time of 30 minutes is 0.5 hours, not 30.
Why do I keep getting the time saved wrong?
Usually because you have reported one of the two journey times instead of the difference between them. Work out both times and subtract the faster one from the slower one.
