Decision and conditions
Translate moving objects and mixed consumption into consistent rates. Speeds are constant and units agree; relative motion depends on direction.
Worked example
A boat moves at 9 km/h in still water; the current is 3 km/h. How many hours does it need to travel 12 km upstream and 12 km downstream? Upstream speed is 6 km/h, so that leg takes 2 hours. Downstream speed is 12, taking 12/12 hours. Total time is 3 hours. Method choice: Current subtracts upstream and adds downstream; add travel times, not speeds.
Contrast: change the reasoning
Two trains of lengths 300 m and 100 m travel toward each other at 10 m/s and 15 m/s. From first contact, how many seconds until they completely pass? Combined length is 400 m. Relative speed is 25 m/s. Time is 400/25=16 seconds. Method choice: The separation to clear is the sum of lengths and the closing speed is the sum of speeds.
Transfer with solution
Two runners start together around a circular track of length 360 m, moving in the same direction at 8 m/s and 5 m/s. After how many seconds does the faster runner first lap the slower one? Relative speed is 8−5=3 m/s. The required relative distance is 360 m. Time is 360/3=120 seconds. Method choice: A full lap relative to the other runner requires gaining one track length.
Boundary check
A car travels 90 highway miles at 30 miles per gallon and 60 city miles at 20 miles per gallon. What is its overall fuel efficiency in miles per gallon? Highway fuel is 3 gallons and city fuel is 3 gallons. Total distance is 150 miles and fuel is 6 gallons. Efficiency is 25 miles per gallon. Method choice: Compute total fuel used, then divide total distance by that fuel.
Misconception to reject
Passing a train requires clearing both lengths, not only reaching its front. Uses still-water speed for the entire journey.
A boat moves at 9 km/h in still water; the current is 3 km/h. How many hours does it need to travel 12 km upstream and 12 km downstream?
- Upstream speed is 6 km/h, so that leg takes 2 hours.
- Downstream speed is 12, taking 12/12 hours.
- Total time is 3 hours.
Compare the other answer choices
Uses downstream speed for both legs.
Uses upstream speed for both legs.
Uses still-water speed for the entire journey.
Divides one leg distance by still-water speed, omitting the second leg.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
GMAT exam content