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 the quant section — one or two marks — and it is worth learning precisely because it is formulaic. 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 40s easy, 50s medium and 65s 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.
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 km/h 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 ComputePrep 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 16 km/h and upstream at 8 km/h.
What is the speed of the boat in still water?
A boat's speed in still water is 14 km/h and the stream flows at 3 km/h.
It travels upstream for 3 hours.
How far does it go?
A boat's speed in still water is 5 km/h and the stream flows at 1 km/h.
It travels downstream for 2 hours.
How far does it go?
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 km/h with times in minutes need one of them converted. As everywhere in this section, convert at the point of reading.
Take half the difference between the downstream and upstream speeds. A boat doing 30 km/h downstream and 20 km/h upstream sits in a current of (30 − 20)/2 = 5 km/h, and its own still-water speed is the average, 25 km/h. 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.
They appear as one or two marks fairly reliably, usually as a single question rather than a set. Given that two relationships cover nearly all of them, the time-to-marks return on learning the topic properly is high.
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