How do I know which form of the formula to use — d = rt, r = d/t, or t = d/r?

All three are the same formula rearranged. Choose the version where what you are solving for is alone on the left side: use d = rt if finding distance, r = \frac{d}{t} if finding rate, and t = \frac{d}{r} if finding time.

What if the speed is given in miles per hour but the time is in minutes?

You must convert one to match the other. If rate is in miles per hour, convert time to hours by dividing minutes by 60. If you prefer working in minutes, convert the rate to miles per minute first. Choose whichever is easier for the numbers given.

Can I use this formula if the object is speeding up or slowing down?

No; d = rt assumes constant speed throughout. If speed changes, you would need calculus or physics, or you can calculate an average speed and treat it as constant for an approximate answer.

Why is distance proportional to time if rate is constant?

In d = rt, if rate is constant and time increases, distance increases by the same factor. This direct proportional relationship is why the graph of distance versus time is a straight line through the origin.

Distance Rate Time

Calculate distance, rate, or time in any uniform motion problem using the formula d = rt, where distance equals rate multiplied by time.

d = rt

Solve a problem with Distance Rate Time

Type the problem. The solver will use Distance Rate Time where Distance Rate Time is the right tool, and tell you when it is not.

What each symbol means

What Distance Rate Time takes

Symbol	Meaning
$d$	Distance is the total length traveled, measured in units like miles or kilometers; confusing it with displacement or forgetting to account for direction can lead to errors.
$r$	Rate (or speed) is how far something travels per unit time, written as miles per hour or similar; reversing which value goes in the numerator and denominator of the rate breaks the formula.
$t$	Time is the duration of travel in hours, minutes, or seconds; forgetting to convert to matching units when rate and time use different scales makes the answer wrong.

When to use it

Use distance-rate-time whenever you need to find how far something travels, how fast it goes, or how long the trip takes at constant speed.

Level

Usually taught in: Pre-Algebra · Appears on: SAT, ACT

Worked examples

1. Find distance traveled

Problem

A car drives at 60 miles per hour for 3 hours. How far did it travel?

$d = rt$
Write the distance-rate-time formula.
$d = 60 \cdot 3$
Substitute the given rate (60 mph) and time (3 hours).
$d = 180$
Multiply $60 \cdot 3 = 180$ to find the distance.

Answer: $d = 180 \text{ miles}$

We substitute the given rate and time directly into the formula and multiply. This is the most basic use of the distance-rate-time relationship.

2. Find rate from distance and time

Problem

A runner covers 15 kilometers in 1.5 hours at constant speed. What is the runner's average speed?

$d = rt$
Start with the distance-rate-time formula.
$r = \frac{d}{t}$
Rearrange by dividing both sides by $t$ to solve for rate.
$r = \frac{15}{1.5}$
Substitute distance 15 km and time 1.5 hours.
$r = 10$
Divide: $15 \div 1.5 = 10$ .

Answer: $r = 10 \text{ km/h}$

When finding rate, rearrange to $r = \frac{d}{t}$ and divide distance by time. This version is useful in sports or travel problems where distance and duration are measured but speed is unknown.

3. Two-leg road trip with different speeds

Problem

On a road trip, Maya drives at 55 mph for 2 hours, then at 70 mph for 3 hours. What is the total distance she traveled?

$d_1 = 55 \cdot 2 = 110$
Calculate the distance for the first leg using $d = rt$ .
$d_2 = 70 \cdot 3 = 210$
Calculate the distance for the second leg.
$d_{\text{total}} = 110 + 210 = 320$
Add both distances to find the total distance traveled.

Answer: $d_{\text{total}} = 320 \text{ miles}$

For trips with multiple legs at different speeds, apply $d = rt$ to each segment separately, then add them together. Never average the speeds first unless the distances are equal.

Common mistakes

Where Distance Rate Time usually goes wrong

The mistake	Why it is wrong	The fix
A car travels at 120 miles per hour for 2 hours and 30 minutes, and a student calculates $d = 120 \cdot 2 = 240$ miles.	The rate is in miles per hour but the time mixes hours and minutes; the formula requires matching units.	Convert 2 hours 30 minutes to 2.5 hours, then calculate $d = 120 \cdot 2.5 = 300$ miles.
Given rate = 50 mph and time = 4 hours, a student calculates $d = \frac{50}{4} = 12.5$ miles.	The formula $d = rt$ requires multiplication, not division; dividing gives a result that is far too small to be realistic.	Multiply instead: $d = 50 \cdot 4 = 200$ miles.
A driver travels 60 mph for 2 hours, then 80 mph for 3 hours, and calculates $d = 70 \cdot 5 = 350$ miles by averaging the speeds.	The formula $d = rt$ applies at each constant rate separately; averaging rates and applying that average to the total time only works if the distances traveled at each speed are equal.	Calculate each leg separately: $d_1 = 60 \cdot 2 = 120$ and $d_2 = 80 \cdot 3 = 240$ , then add: $d = 120 + 240 = 360$ miles.

Tips and when to use something else

Remember the three forms: $d = rt$ (finding distance), $r = \frac{d}{t}$ (finding rate), and $t = \frac{d}{r}$ (finding time) — pick the one with what you seek isolated on the left.
Always check that rate and time use compatible units before substituting; convert minutes to hours or vice versa as needed.
For trips with multiple segments at different speeds, apply $d = rt$ to each segment separately and then add; never average the speeds first.
If the object is accelerating or decelerating, use Work Rate Problems or physics equations instead of this formula, which requires constant speed.

Related formulas

Literal EquationsLiteral equations rearrange formulas to solve for any variable, letting you find missing measurements when you know the others.Unit RateA unit rate is a ratio that compares a quantity to exactly one unit of measure, helping you compare values or find the cost per item.Linear EquationSolve for the value of x in any linear equation by rearranging to isolate x, finding the unique solution where the expression equals zero.

Frequently asked questions

How do I know which form of the formula to use — d = rt, r = d/t, or t = d/r?: All three are the same formula rearranged. Choose the version where what you are solving for is alone on the left side: use $d = rt$ if finding distance, $r = \frac{d}{t}$ if finding rate, and $t = \frac{d}{r}$ if finding time.
What if the speed is given in miles per hour but the time is in minutes?: You must convert one to match the other. If rate is in miles per hour, convert time to hours by dividing minutes by 60. If you prefer working in minutes, convert the rate to miles per minute first. Choose whichever is easier for the numbers given.
Can I use this formula if the object is speeding up or slowing down?: No; $d = rt$ assumes constant speed throughout. If speed changes, you would need calculus or physics, or you can calculate an average speed and treat it as constant for an approximate answer.
Why is distance proportional to time if rate is constant?: In $d = rt$ , if rate is constant and time increases, distance increases by the same factor. This direct proportional relationship is why the graph of distance versus time is a straight line through the origin.

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Reviewed 2026-09-18