 # How do you work out distance, speed and time?

These are often set as questions in maths tests but are useful for us to know so that we can approximate how long a journey will take.

There’s a simple formula which governs the three, and it can be expressed with either variable as the subject of the equation:

Distance = speed * time

Time = distance/speed

Speed = distance/time

So, as long as we have a couple of those, we can plug them into one of the equations.

## How to calculate distance travelled

Let’s have a couple of examples:

You’re going to drive at an average of 70km/h for 4 hours.

Distance is speed multiplied by time, so:

70km/h * 4 hours = 280km.

Easy so far, but what about if you’re going to be driving for 4 hours and 15 minutes? Now you either need to figure out how much 15 minutes is as a decimal number of hours, or you need to convert the hours figure into minutes and, at the end, convert it back.

The first option is fairly simple: take the 15 minutes and divide it by 60 minutes so that we know what proportion of an hour 15 minutes is.

15 minutes / 60 minutes = 0.25 hours

Add that onto the 4 hours you already have and it’s 4.25 hours. Plug it into the same equation:

70km/h * 4.25 hours = 297.5km

The other way around of doing this is converting the time into minutes. Four hours in minutes is 4 * 60 = 240 minutes.

Add the 15 minutes and we have 255 minutes.

Now, when we do the equation, it’s going to give us the wrong figure because our speed is in kilometres per hour, but our time is in minutes. That will totally mess you up. You have to make sure you’re speaking in the same time units. Let’s try it:

70km/h * 255 minutes = 17850 of some figure that makes no sense!

It’s a good hint in an equation that if it looks wrong, it probably is.

What do we do? Well, there are two ways:

1. convert kilometres per hour to kilometres per minute (70km/h / 60 minutes = 1.17km/min), therefore 1.7km/min * 255 minutes = 297.5km
2. or convert 255 minutes to a decimal hour by doing 255 minutes / 60 minutes = 4.25 hours, which gives us the figure we had before.

One more example: You’re travelling at 100km/h. How far, in metres, do you travel in five seconds?

Again, we have to make sure we’re talking about the same units. We have 100km/h, but time unit is in seconds and the final answer is in metres. First we have to convert 100km/h. If we divide it by 60, then we convert it to minutes

100km/h / 60 minutes = 1.667km/minute

We might now want to convert the kilometres into metres which can be done by multiple by 1000.

1.66667km/minute * 1000 = 1666.67m/minute.

Right, but we’re still talking in minutes, so let’s convert it to seconds:

1666.67m/minute / 60 seconds = 27.78metres per second (27.78m/s)

Now we’re talking in the same units as the original question. We just need to figure out how many we travel in 5 seconds.

Distance = speed * time, therefore distance = 27.78 * 5 = 138.89 metres.

## How to calculate average speed

Speed is distance divided by time. Simply put, if you drove 60 kilometres for one hour, it would look like this:

Speed = distance (60 km) / time (1 hour) = 60km/h.

Let’s take a more complex example: what’s the average speed if you covered 425.5km in 5 hours 22 minutes and 30 seconds?

Firstly, we have the problem again with the time not being decimalised. We can use the same method we did before:

30 seconds / 60 seconds is 0.5. This means 30 seconds is 0.5 minutes. Therefore we add that the 22 minutes and repeat it again:

22.5 minutes / 60 minutes = 0.375 hours. Add that onto the 5 hours and you have 5.375 hours.

Speed = distance (425.5km) / time (5.375 hours) = 79.16km/h

## How to calculate time taken to cover a distance

Our final variation is calculating how much time it takes when you know the distance and the speed.

Time = distance/speed. So, a nice easy one would be how many hours does it take to cover 30km when you are travelling at 120km/h.

Time = 30km/120km/h = 0.25 hours.

If you need to figure out how many minutes that is, simply multiply it by 60, which gives you 15 minutes.

Taking a more complex example, if you’re travelling the 842km from Picton to Gore, how long in hours, minutes and seconds will it take you if you average 67km/h?

Time = 842km / 67km/h = 12.5672 hours

Let’s convert that decimal to minutes and seconds. Firstly, multiply 0.5672 by 60 = 34.0299 minutes. Now we multiply that decimal by 60 to get seconds: 0.0299 * 60 = 1.8 seconds. We can round that up to 2 seconds, which gives us 12 hours, 34 minutes and 2 seconds.

Now you know how to do the conversion for speed, distance and time. Darren is a member of the Institute of Advanced Motorists and the NZ Motoring Writers' Guild