Boats & Streams · Topic 1 of 5

🚣 Boats & Streams Basics

2 exam question types, fully solved

Every boats-and-streams question is built from just two hidden numbers: the boat's own speed in still water (call it ) and the speed of the moving water, the stream (call it ). Once you can write down these two, every question becomes simple arithmetic.

The two speeds, and how to recover them

Going downstream the current pushes the boat, so the speeds add: . Going upstream the current fights the boat, so they subtract: . Upstream is therefore always the slower, longer leg.

Turn that around to get the two hidden numbers from the two effective speeds: the boat speed is the average of the two, and the stream is half their difference:

· .

• Speed ratio: the boat-to-stream ratio is , so any percentage or ratio between the up/down speeds converts straight into .

• Same distance each way: time is inversely proportional to speed, so — the slower upstream leg always takes the bigger share of time.

⛵Boats & Streams SimulatorSet speeds · press a direction · watch the boat!

Boat speed (B) in still water

km/h

Stream speed (S / current)

km/h

Downstream (→)B + S = 14 km/h

Upstream (←)B − S = 6 km/h

Time comparison — enter a distancekm

DOWNSTREAM TIME

4.29 h

60 ÷ 14

UPSTREAM TIME

10.00 h

60 ÷ 6

Find boat & stream speed from U and D

U (upstream):km/h

D (downstream):km/h

Boat speed = (U+D)/2

10.00 km/h

Stream speed = (D−U)/2

4.00 km/h

If upstream speed is 6 km/h and downstream is 14 km/h, the boat's still-water speed is = km/h.

Q1A boat rows at 12 km/h in still water on a stream of 4 km/h. Its downstream speed is:

Q2A boat goes 6 km/h upstream and 14 km/h downstream. Its speed in still water is:

Q3A boat goes 4 km/h upstream and 10 km/h downstream. The speed of the stream is:

📚

Real exam questions — Boats & Streams Basics

2 question types · 8 solved examples from real SSC papers

In boats and streams, a boat's downstream speed is its still-water speed plus the stream and its upstream speed is still-water minus the stream — master that one idea and the whole topic falls into place.

How to solve this type

Call the boat's speed in still water

b

and the stream speed

s

. Going with the current the speeds add, so downstream

D=b+s

; going against it they subtract, so upstream

U=b-s

. Reverse these to recover the two unknowns:

b=\dfrac{D+U}{2}

and

s=\dfrac{D-U}{2}

(boat

=

the average of the two speeds, stream

=

half their difference). For a FIXED distance, time is inversely proportional to speed, so

T_U:T_D = D:U

. Two shortcuts worth memorising: if the boat speed is

n

times the stream speed then

D:U=(n+1):(n-1)

; and if the upstream time is

n

times the downstream time then

\dfrac{b}{s}=\dfrac{n+1}{n-1}

. The fast route is always to turn the given ratio or percentage into clean unit-parts rather than setting up heavy algebra.

The speed of a boat in still water is twice the speed of the stream. The boat covers a certain distance downstream in 3 hours. How long will it take to cover the same distance upstream?

A6 hB9 hC12 hD15 h

The downstream speed of a boat is 150% of its upstream speed. If the speed of the boat in still water is 10 km/h, find the speed of the stream.

A2 km/hB3 km/hC4 km/hD5 km/h

The downstream speed of a boat is 125% of its speed in still water. If the boat's speed in still water is 40 km/h, what is the speed of the stream?

A8 km/hB10 km/hC12 km/hD15 km/h

The ratio of the speed of a boat in still water to the speed of the current is 31:6. The boat covers a distance downstream in 4 hours 10 minutes. How long will it take to return (cover the same distance upstream)?

A4 h 10 minB5 h 10 minC5 h 50 minD6 h 10 min