How to Solve Distance, Rate, and Time Problems: Step-by-Step for 2026
Distance-rate-time problems are the classic source of test anxiety in Algebra 1. Two trains, two cars, a boat in a river, a plane with a tailwind. They all sound like trick questions until you see the pattern. There is one formula, one organizing chart, and three sub-types. Once you have those, every DRT problem on every test follows the same routine.
This guide covers the DRT formula, the chart method that prevents errors, and worked examples of every sub-type.
The DRT Formula
\[d = r \cdot t\]
Distance equals rate times time. The two rearrangements:
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r = d / t (rate equals distance divided by time).
t = d / r (time equals distance divided by rate).
The units must match. If rate is in miles per hour and time is in minutes, convert one of them before multiplying.
The Chart Method
Every multi-mover problem fits in this table:
Mover
Rate
Time
Distance
A
B
Fill in any two columns from the problem, then use d = rt to fill the third. The equation almost always comes from a relationship between the two distances or two times.
Type 1: Same Direction (Catching Up)
Maria leaves home jogging at 6 mph. Two hours later, her brother bikes after her at 14 mph. How long until her brother catches up?
Let t = time the brother bikes. Maria has been moving for t + 2 hours.
Mover
Rate
Time
Distance
Maria
6
t + 2
6(t + 2)
Brother
14
t
14t
They have traveled the same distance when he catches up:
Two trains leave the same station at the same time, heading in opposite directions. One travels at 50 mph, the other at 70 mph. After how many hours are they 360 miles apart?
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With (downstream / tailwind): rate is s + w.
Against (upstream / headwind): rate is s − w.
A plane flies 600 miles with the wind in 2 hours and the same distance against the wind in 3 hours. Find the plane’s still speed and the wind speed.
Two equations:
– With wind: (s + w)(2) = 600 → s + w = 300.
– Against wind: (s − w)(3) = 600 → s − w = 200.
Add the equations: 2s = 500 → s = 250 mph. Then w = 50 mph.
Common Mistakes
Mixing units. Convert minutes to hours, or miles to feet, before multiplying.
Averaging rates without weighting by time. Always go total distance over total time.
Forgetting the head start. When one mover leaves early, that mover’s time variable is t + (head start), not t.
Adding distances when they should be set equal. Same direction: distances are equal at catch-up. Opposite directions: distances add to total.
Skipping the chart. Without the chart, sign errors and equation-setup errors triple.
A Quick Cheat Sheet
Situation
Equation
Catch up (same direction)
d_A = d_B
Meet or apart (opposite directions)
d_A + d_B = total
Round trip
t_down + t_up = total time
Average rate
total distance / total time
Wind / current
rate = still ± wind
Tape this inside the front cover of your binder.
Frequently Asked Questions
Do I have to use the chart?
No, but you should until the problems become automatic. It prevents 90 percent of setup errors.
What units should I use?
Whatever the problem gives you, as long as they match. If the answer needs different units (minutes instead of hours), convert at the end.
Are these problems on the SAT?
Yes. Several DRT items show up on every Digital SAT, especially average rate and same-direction catch-up.
What is the most-missed DRT problem?
Average rate. Most students average the two speeds. The correct method is total distance over total time.
How fast should I be at these by test day?
A clean two-mover problem should take 90 seconds, including the chart. Three minutes for the wind / current type.
Closing Thought
Distance, rate, and time problems are a single formula, an organizing chart, and six sub-types. Drill three problems of each type and your speed doubles. Watch the units, watch the head starts, and never average rates without weighting by time.
For more practice, browse our Algebra 1 worksheets and our full Math Topics library. When you are ready for a structured workbook, our Algebra 1 collection covers every word-problem type above.
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