Speed, Distance, Time — Formula Triangle & Problems

Use the speed, distance, and time formula when the speed is constant, or when a problem gives the average speed for the whole trip. The core relationship is

$$d = st$$

where $d$ is distance, $s$ is speed, and $t$ is time. Rearranging gives the other two formulas:

$$s = \frac{d}{t}, \qquad t = \frac{d}{s}$$

If you remember those three equations and keep the units consistent, you can solve most school-level speed, distance, and time problems quickly.

Speed, Distance, And Time Formulas

• Distance: $d = st$
• Speed: $s = d/t$
• Time: $t = d/s$

The formulas are all versions of the same relationship. Start with $d = st$, then rearrange depending on what the question asks for.

This only works directly if the speed stays constant during the motion, or if the problem clearly says to use average speed.

How The Formula Triangle Helps

Many students use a formula triangle to remember which operation to use. Put $d$ on top and place $s$ and $t$ underneath.

If you cover $d$, you multiply the two bottom quantities, so $d = st$. If you cover $s$, you get $d/t$. If you cover $t$, you get $d/s$.

The triangle is just a memory aid. The actual math comes from rearranging $d = st$.

What The Variables Mean

• Speed tells you how much distance is covered per unit of time.
• Distance tells you how far something travels.
• Time tells you how long the motion lasts.

Units matter as much as the formula. If speed is in kilometers per hour, use hours for time if you want the distance in kilometers. If the units do not match, convert before you calculate.

Worked Speed, Distance, Time Example

A bus travels $150$ kilometers at a constant speed of $60$ kilometers per hour. How long does the trip take?

We need time, so use $t = d/s$.

$$t = \frac{150}{60} = 2.5$$

So the trip takes $2.5$ hours, which is $2$ hours $30$ minutes.

The answer makes sense. At $60$ km/h, the bus covers about $60$ kilometers each hour, so a $150$ kilometer trip should take a little more than $2$ hours.

Common Speed, Distance, Time Mistakes

Mixing units

If distance is in meters and speed is in kilometers per hour, the calculation will be wrong unless you convert first.

Using the wrong formula

For time, use $t = d/s$, not $t = s/d$. A quick unit check helps: distance divided by speed gives time.

Ignoring the constant-speed condition

If the speed changes during the trip, you cannot use one segment speed for the whole journey unless the problem says the speed is constant or gives the average speed for the full trip.

When You Use This Formula

This relationship appears in travel problems, race questions, journey planning, and many unit-rate problems. It is also a starting point in physics before motion becomes more complicated.

If acceleration matters, speed is no longer constant, so this model is only part of the story. For many basic problems, though, it is the right first tool.

Try A Similar Problem

Try a similar problem: a cyclist travels $36$ miles at $12$ miles per hour. First find the time. Then change the speed to $9$ miles per hour and see how the answer changes.