SAT Math: Rate Problems (Speed, Distance, Time)
34+ practice questions in Praczo
The concept, explained
- 1
Core formula: Distance = Rate × Time (d = rt). The rearrangements Rate = d/t and Time = d/r are equally important.
- 2
For multi-segment trips, set up a separate d = rt for each segment and combine using the total constraint (total time or total distance).
- 3
Average speed for a round trip or multi-segment journey = total distance ÷ total time. Do NOT average the two speeds.
- 4
Work-rate problems use the same logic: if A completes a job in 3 hours, A's rate is 1/3 job per hour. Add rates to find combined time: 1/3 + 1/4 = 7/12, so together they finish in 12/7 hours.
- 5
Always check units — if speed is miles per hour but time is given in minutes, convert before calculating.
- ✗ Averaging two speeds to find average speed. Drive 60 mph there and 40 mph back — average speed is NOT 50 mph. Compute total distance / total time.
- ✗ Adding times instead of rates in work problems. Add the individual rates (1/t), not the times.
SAT-style practice
A car travels 120 miles at 60 mph, then returns the same 120 miles at 40 mph. What is the average speed for the entire trip?
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