Distance, Rate, and Time Formula
Use d = rt to solve distance, speed, and time problems.
Includes examples for travel, running, and everyday scenarios.
The Formula
This is one of the most fundamental and widely used formulas in math and everyday life. It relates distance traveled, the rate of travel (speed), and the time spent traveling.
Variables
| Symbol | Meaning |
|---|---|
| d | Distance traveled (miles, km, meters, etc.) |
| r | Rate of speed (mph, km/h, m/s, etc.) |
| t | Time spent traveling (hours, minutes, seconds, etc.) |
Three Forms of the Formula
You can rearrange the formula to solve for any variable:
| Solve For | Formula |
|---|---|
| Distance | d = r × t |
| Rate (speed) | r = d / t |
| Time | t = d / r |
Example 1 — Finding Distance
A car drives at 60 mph for 2.5 hours. How far does it go?
d = r × t
d = 60 × 2.5
d = 150 miles
Example 2 — Finding Speed
A runner completes a 10 km race in 50 minutes. What is their average speed?
r = d / t
t = 50 minutes = 0.833 hours
r = 10 / 0.833
r = 12 km/h (about 7.5 mph)
Example 3 — Finding Time
A plane flies 2,400 miles at 500 mph. How long is the flight?
t = d / r
t = 2400 / 500
t = 4.8 hours (4 hours 48 minutes)
Example 4 — Metric Units
A cyclist rides at 25 km/h for 1 hour 15 minutes. How far?
t = 1 hour 15 min = 1.25 hours
d = 25 × 1.25
d = 31.25 km (about 19.4 miles)
When to Use It
- Planning road trips and estimating arrival times
- Calculating running or cycling pace
- Figuring out how fast you need to go to arrive on time
- Physics problems involving constant velocity (no acceleration)
- Comparing travel options (driving vs. flying time)
Important Notes
- Units must be consistent — if speed is in km/h, time must be in hours, and distance will be in km.
- This formula assumes constant speed. For changing speeds, use average speed or kinematic equations.
- To convert minutes to hours, divide by 60. To convert hours to minutes, multiply by 60.