Boats & streams
Boat and stream questions give a boat's speed in still water and a current, and ask for time or distance. Downstream speed is boat plus stream; upstream is boat minus stream. Given both, the boat's speed is their average and the stream's speed is half their difference — which answers most exam questions in one line.
Boats and streams is a small, entirely formulaic corner of timed quant, and it is worth learning precisely because it is formulaic. It is not on GRE or GMAT Practice — Other keeps it — and the shared daily does not serve it. The same two relationships answer nearly every question, and the questions that look different are usually time-speed-distance problems wearing a boat.
Try it against the clock. Boats & Streams runs at 90s easy, 105s medium and 120s hard. The clock is stamped and judged on our server, so the limit you see is the deadline that is actually enforced — and it starts when you tap Start, not while the question is loading.
This format is not on GRE or GMAT Practice. The drill link opens it on the Other track, which keeps the full library. If you already chose GRE or GMAT, switch to Other in Settings. The shared daily does not serve it.
Downstream = b + s, upstream = b − s. Writing these two lines first turns almost every question into substitution rather than reasoning, and it stops the direction confusion that costs the marks.
If downstream and upstream speeds are known, b is their average and s is half their difference. A boat covering 30 miles per hour downstream and 20 upstream has a still-water speed of 25 and a current of 5. That is the single most-asked relationship in the topic.
Questions usually give times for a fixed distance rather than speeds. Divide distance by time to get each speed first; comparing times directly gives the inverse relationship and the wrong answer.
Averaging the upstream and downstream times and dividing distance by that does not give the still-water speed. Convert to speeds, then average. This is the one genuine trap the topic contains.
| Given | Then |
|---|---|
| Boat b, stream s | Downstream b + s, upstream b − s |
| Downstream d, upstream u | Boat = (d + u)/2 |
| Downstream d, upstream u | Stream = (d − u)/2 |
| Same distance both ways | Time ratio is the inverse of the speed ratio |
| Still water time vs downstream time | Difference comes entirely from s |
| Stream speed 0 | Reduces to ordinary time-speed-distance |
Generated by the same engine that mints the Quant Daily daily. Each answer is computed from the numbers printed in the question, and the walkthrough below each one is the engine's own working — not a solution written afterwards. Reload this page's live drill and you get different numbers.
A boat travels downstream at 20 miles per hour and upstream at 12 miles per hour.
What is the speed of the boat in still water?
A boat's speed in still water is 14 miles per hour and the stream flows at 6 miles per hour.
It travels downstream for 3 hours.
How far does it go?
A boat travels downstream at 14 miles per hour and upstream at 6 miles per hour.
What is the speed of the boat in still water?
The wrong options are not random numbers. Each one is the result of a specific careless error for this topic, so picking one tells you which habit is costing you marks.
The still-water speed is the average of the upstream and downstream SPEEDS. Averaging times and converting afterwards produces a plausible number that is wrong, and it is always an option.
Downstream travels with the current and is therefore faster. Writing both formulas down before starting makes this mechanical rather than something to recall under pressure.
Speeds in miles per hour with times in minutes need one of them converted. As everywhere in this section, convert at the point of reading.
The specific wrong numbers this topic produces, and what each one tells you about the step you took. If you have just got a question wrong and want to know which habit did it, start here.
No. Times cannot be averaged; speeds can. Work out the two speeds from the distance first, then use still-water speed = (downstream + upstream) ÷ 2 and stream speed = (downstream − upstream) ÷ 2. Averaging the times gives a number close enough to look right and it is printed as an option.
Downstream is with the current, so it is the larger speed, b + s. Upstream is against it, b − s. The check is instant: if your stream speed comes out negative, you have the two the wrong way round, because a stream never flows backwards in these questions.
Everywhere the two meet. Convert the minutes to hours before dividing: 45 minutes is 3/4 of an hour, not 0.45. A question that pairs a boat's speed in miles per hour with a forty-minute leg is testing the conversion just as much as the formula.
Take half the difference between the downstream and upstream speeds. A boat doing 30 miles per hour downstream and 20 upstream sits in a current of (30 − 20)/2 = 5 miles per hour, and its own still-water speed is the average, 25. Those two lines answer most questions in this topic.
Because time is inversely proportional to speed, so the average of two times does not correspond to the average of the two speeds. Convert each time into a speed first, average those, and then convert back if the question wants a time.
No. Both tracks hide this format, and the shared daily does not serve it. Other keeps it. Two relationships still cover nearly every question of this shape.
Quant Daily is free, needs no account, and is not affiliated with ETS or GMAC. Not on GRE or GMAT Practice. Other keeps this format.
