How to Solve Speed Distance Time Problems (With Examples)

I was standing at a bus stop doing math on my phone… and it looked wrong

I was waiting for a bus that was “8 minutes away” (according to the app), staring down the road, and doing that little mental physics game we all do: Okay, if it’s about 2.4 km away and it’s coming at… what, 30 km/h? And my numbers weren’t even close. I kept getting something like 5 minutes, then 12 minutes, then I realized I’d mixed units and also kind of lied to myself about the speed.

So yeah, speed–distance–time problems are simple… until they aren’t.

If you’ve ever stared at a word problem like “a cyclist travels…” and felt your brain quietly leave the room, you’re not alone. The trick isn’t memorizing anything fancy. It’s picking the right formula, keeping units consistent, and not letting the story part of the problem mess with you.

The only relationship you really need (and why it keeps working)

Speed, distance, and time are tied together in a way that’s almost annoyingly neat. If you move at a steady speed, you cover the same amount of distance every unit of time. That’s it. That’s the whole vibe.

And the reason this keeps showing up is because it’s basically the definition of average speed for constant motion. Not “physics magic.” Just “how fast” means “how much distance per time.”

But here’s the part people quietly mess up: you can’t divide kilometers by seconds and expect a nice answer unless you want km/s. Same with minutes and meters. The math will still run, but the answer will feel cursed.

So pick a unit system first. Then stay loyal to it.

And if you want a quick helper, I built these so you don’t have to keep reinventing the wheel: speed calculator,

One more thing before examples: a lot of homework problems say “speed” but secretly mean “average speed,” especially if there are multiple legs of a trip. We’ll hit that in a second.

Examples that actually feel like real life (and how to not get tricked)

Okay, now the fun part. I’m going to do these like I’d do them on scratch paper: write what you know, pick units, plug in, sanity-check. Not because that’s “proper,” but because it saves you when the problem is wordy or sneaky.

Also: I’m going to say “speed” for simplicity, but if direction matters you’d call it velocity. Most speed–distance–time homework problems don’t care about direction unless they explicitly talk about vectors, north/south, positive/negative, or something like that.

Example 1: Solve for speed.

A runner covers 1500 m in 6 minutes. What’s their average speed in m/s?

Write down what you’ve got:

• d = 1500 m
• t = 6 minutes = 360 s (because 6 × 60)

Now use v = d / t:

v = 1500 / 360 ≈ 4.17 m/s

That’s a believable running speed (fast-ish but not absurd). If you got 41.7 m/s, you’d know you messed up a unit, because that’s more like a car on a city street.

Example 2: Solve for time.

A car travels 90 km at 60 km/h. How long does it take?

Here the units already match (km and km/h), so don’t “fix” them unless the question asks for minutes or seconds.

• d = 90 km
• v = 60 km/h

t = d / v = 90 / 60 = 1.5 h

And 1.5 hours is 1 hour 30 minutes.

This is one of those where people overthink it and start converting everything into meters and seconds “because physics.” You can, but you don’t have to.

Example 3: Solve for distance.

A bike moves at about 5 m/s for 12 seconds. How far does it go?

• v = 5 m/s
• t = 12 s

d = v·t = 5 × 12 = 60 m

Quick sanity-check: 5 m/s is about a brisk bike pace, 12 seconds isn’t long, so 60 m feels right.

Example 4 (the one that trips people): average speed over multiple legs.

You drive 30 km at 60 km/h, then another 30 km at 30 km/h. What’s your average speed for the whole trip?

This is where a lot of students do this:

(60 + 30) / 2 = 45 km/h

And honestly, I get why. It’s a tempting little average. But it’s wrong because you spend different amounts of time at each speed. The slower part eats more time.

Do it the boring-but-correct way: total distance / total time.

• Leg 1 time: t1 = 30/60 = 0.5 h
• Leg 2 time: t2 = 30/30 = 1 h
• Total distance: d = 60 km
• Total time: t = 1.5 h

Average speed v_avg = 60 / 1.5 = 40 km/h

See how it drops below 45? That’s the “time weighting” showing up.

And if you want to check yourself quickly, you can punch it into the average speed calculator and compare your scratch work (I do that all the time, especially when I’m tired).

So why does everyone get this wrong? Because our brains want symmetry, and the trip doesn’t have it.

Here’s a little unit cheat sheet I keep in my head (and I still mess it up sometimes).

If you don’t want to do the 3.6 thing in your head, use the converter: km/h to m/s converter or m/s to km/h converter. (No shame. I built them for a reason.)

And yeah, here’s an embedded one you can poke at while you work problems:

The little checklist I run every single time

I don’t care if you’re doing a middle-school worksheet or a college lab. This checklist catches most mistakes.

Write down what the problem is actually asking.

• Circle the knowns: distance, time, speed. If one is missing, that’s probably what you’re solving for.
• Pick units you can live with. If the problem uses km and hours, you can stay there. If it mixes minutes and meters, convert.
• Use the right rearrangement: v = d/t, d = v·t, t = d/v.
• Sanity-check: does your answer feel like a human speed, a car speed, a plane speed? If a person is “running” at 25 m/s, something went sideways.

And if the problem has multiple parts (stops, different speeds, turnarounds), don’t average speeds unless the distances and times make it legit. Total distance over total time is the safe path.

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