The distance-rate-time formula is d = rt: distance equals rate (speed) times time, for anything moving at a constant rate. Solve it for the other two letters to get r = dt and t = dr. Driving at 45 miles per hour for 3 hours covers 45 × 3 = 135 miles.
In Spanish
fórmula de distancia, velocidad y tiempo
Also called
d = rt, distance formula (motion), distance equals rate times time, DRT formula
Cover the quantity you want: d on top means multiply r × t; r or t on the bottom means divide d by the other one. At 45 mph, each hour adds 45 miles.
Formal definition and notation
For an object moving at a constant rate r for an elapsed timet, the distance traveled is d = rt, with the units of r matching the units of d per unit of t. Because it is one equation in three quantities, any two of them determine the third: r = dt for t ≠ 0 and t = dr for r ≠ 0. It is the formula listed as distance on the GED formula sheet.
A train covers 210 kilometers at 84 kilometers per hour. How long does the trip take, in hours and minutes?
Solve for time: t = dr.
t = 21084 = 2.5 hours.
0.5 hour is 0.5 × 60 = 30 minutes.
Answer: The trip takes 2.5 hours, which is 2 hours 30 minutes.
Example 3: Two cars, opposite directions
Test-style
Two cars leave the same town at the same time and drive in opposite directions, one at 50 mph and one at 60 mph. After how many hours are they 330 miles apart?
Each hour the gap grows by 50 + 60 = 110 miles.
Set up d = rt for the gap: 330 = 110t.
Divide: t = 330 ÷ 110 = 3.
Check: 50 × 3 + 60 × 3 = 150 + 180 = 330 miles.
Answer: They are 330 miles apart after 3 hours.
Common mistakes
✗ MistakeDriving 48 mph for 15 minutes: d = 48 × 15 = 720 miles.
✓ Instead15 minutes = 1560 = 0.25 hour, so d = 48 × 0.25 = 12 miles.
The rate is per hour, so the time must be in hours. Mixing minutes with miles per hour gives answers 60 times too large.
✗ MistakeTime for 150 miles at 50 mph: t = 50150 = 13 hour.
✓ Insteadt = dr = 15050 = 3 hours.
Distance goes on top when you solve for time. A quick sense check: at 50 mph, 150 miles must take more than 1 hour.
✗ MistakeTwo hikers walk away from each other at 3 mph and 4 mph, so the gap grows at 4 − 3 = 1 mph.
✓ InsteadMoving apart, the gap grows at 3 + 4 = 7 mph.
Subtract rates only when both move in the same direction. In opposite directions, both distances add to the gap.
The formula d = rt assumes one constant rate. Average speed is total distance over total time for a trip whose speed changed. Use d = rt on each part, then divide the totals.
Distance-Rate-Time Formulavs.Distance formula (coordinates)
In coordinate geometry the distance formula√(x2 − x1)2 + (y2 − y1)2 finds the length between two points. The motion formula d = rt is a different idea.
Rate is one part of the formula: a comparison of two quantities with different units, like 45 miles per hour. The formula ties the rate to a distance and a time.
Quick check: 3 questions
Question 1 of 3
A runner keeps a pace of 8 miles per hour for 1.5 hours. How far does she run?
Show answer and explanation
Answer: B.d = 8 × 1.5 = 12 miles. 9.5 adds the numbers, 5.3 divides 8 by 1.5, and 6.5 subtracts.
Question 2 of 3
How long does it take to drive 195 miles at 60 mph?
Show answer and explanation
Answer: A.t = 19560 = 3.25 hours, and 0.25 hour is 15 minutes. 3 h 25 min reads 3.25 as 3 hours 25 minutes; 0.31 h divides 60 by 195.
Question 3 of 3
Two trains leave a station at the same time, going the same direction at 70 km/h and 85 km/h. How far apart are they after 4 hours?
Show answer and explanation
Answer: C. Same direction, so the gap grows at 85 − 70 = 15 km/h. After 4 hours: 15 × 4 = 60 km. 620 adds the rates, 340 is one train alone, and 15 is the gap after 1 hour.
Is the distance-rate-time formula on the GED formula sheet?
Yes. The GED mathematics formula sheet lists distance as d = rt. The sheet does not give the rearranged forms, so you need to solve for r or t yourself: divide both sides by the quantity you do not want. For example, t = dr.
What is the difference between rate and speed?
Speed is the rate of motion: how far something goes per unit of time. Rate is the wider word for any per-unit comparison, like pages per minute or dollars per hour. In d = rt, the rate is a speed, but the same structure works for any rate: amount = rate × time.
How do you remember the distance-rate-time formula?
Picture a triangle with d on top and r and t on the bottom. Cover the quantity you want: covering d leaves r × t; covering t leaves d over r. Or think of a simple case: 60 mph for 2 hours is 120 miles, so distance must be rate times time.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 6.RP.A.3.b, CCSS HSA-CED.A.4
Cite this entry
Effortless Math Team. “Distance-Rate-Time Formula.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/distance-rate-time-formula/
Flashcard
TermDistance-Rate-Time Formulad = rt
DefinitionDistance equals rate times time, for a constant rate. Also r = dt and t = dr. 50 mph for 3 hours is 150 miles.
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