With the helper
Effective speed = base speed + helper speed.
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GMAT Quant
Average Speed and Motion Variants
Handle average speed, equal-distance trips, currents, mixed units, and staggered starts without common setup errors.
Average speed
Average speed is total distance divided by total time.
Do not average the listed speeds unless the travel times are equal.
Equal-distance out-and-back has a useful shortcut.
- Out speed
- a
- Back speed
- b
- Average speed
- 2ab/(a+b)
- Reason
- Distances are equal, times are not
Example: 72 mph out, 48 mph back, same distance.
- Shortcut
- 2*72*48/(72+48)
- Numerator
- 6912
- Denominator
- 120
- Average speed
- 57.6 mph
Same-distance model
For the same distance, rates and times move inversely.
If two trips cover the same distance, R1*T1 = R2*T2. A faster rate must correspond to a shorter time.
A current or moving surface changes effective speed.
Against the helper
Effective speed = base speed - helper speed.
Units first
Normalize units before using a formula.
- 01Convert minutes to hours when rates are per hour.
- 02Keep distance units consistent.
- 03Distinguish time after departure from clock time.
- 04Use a short timeline when start times differ.
Efficiency
Backsolve when the answer choices make algebra longer than necessary.
If choices are candidate speeds or times, start near the middle choice, test the resulting relationship, then adjust.
Mini application
Try this: a boat moves at 12 km/h in still water and the current is 3 km/h.
What are its downstream and upstream speeds?
Solution
Downstream is 15 km/h; upstream is 9 km/h.
Add the current when it helps and subtract it when it opposes the boat.
Remember this
Use total distance / total time for averages.
Treat average speed as a new rate derived from the whole trip, not as a simple average of the component speeds.