SSC CGL Maths · Time, Speed and Distance

Boats and Streams

The stream adds its speed to a boat going down and takes it away from a boat going up, so the boat's own speed is half the sum of the two and the stream's is half the difference.

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Why this matters

Twenty-three questions in the bank, eleven EASY and twelve MODERATE, and none from the 2025 shifts. The MODERATE ones give two journeys and ask you to untangle two unknown speeds; taking 1 ÷ speed as the unknown turns them into simple straight-line equations.

Concept 1 of 3: Downstream and upstream speeds

In still water a boat moves at its own speed. Downstream the river carries it along, so the two speeds add; upstream the river pushes back, so the stream's speed is taken away. Know any two of the four speeds and you know the other two.

Definition

Downstream $D = b + s$ and upstream $U = b - s$ , where $b$ is the boat's speed in still water and $s$ the stream's.
Boat $b = \frac{D + U}{2}$ and stream $s = \frac{D - U}{2}$ .
"Speed in still water", "rowing speed" and "speed of the boat" all mean $b$ . "With the current" or "along the stream" is downstream; "against" is upstream.
Round trip: time $= \frac{d}{b + s} + \frac{d}{b - s}$ . With $b$ and the total time known, try each option for $s$ : it is faster than solving.
A percentage on speed or time is a ratio: a downstream speed that is 125% of the boat's speed means $D = \frac{5}{4}b$ , so $s = \frac{b}{4}$ .

Boats and streams

D = b + s \qquad U = b - s \qquad b = \frac{D + U}{2} \qquad s = \frac{D - U}{2}

$D$ downstream speed
$U$ upstream speed
$b$ speed of the boat in still water
$s$ speed of the stream

Worked example

A boat goes 42 km downstream in 3 hours and the same 42 km upstream in 7 hours. Find the speed of the boat in still water and the speed of the stream.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 11 Sep 2024, Shift 3 · Q60Easy

Example 1 · Time, Speed and Distance · Boats and Streams

A boat can go 54 km upstream in 6 hours. If the speed of the stream is 4.8 km/h, then how much time (in hours) will the boat take to cover a distance of 279 km downstream?

Forgetting to halve

The stream's speed is HALF the difference of the downstream and upstream speeds, and the boat's is half the sum. The difference itself is twice the stream's speed.

Giving the downstream speed as the boat's speed

The speed of the boat means its speed in still water. The downstream speed already includes the stream, so it is always more than the boat's speed.

Drill 12 more on downstream and upstream speeds

Concept 2 of 3: Boat and stream speeds from a ratio

For the same distance, time is inversely as speed. So the ratio of upstream time to downstream time is the ratio of downstream speed to upstream speed, and half the sum and half the difference work just as well on the parts of a ratio.

Definition

Times over the same distance $t_U : t_D$ give the speeds $D : U = t_U : t_D$ .
Then boat : stream $= (D + U) : (D - U)$ . Times of 8 hours and 5 hours give $13 : 3$ .
Boat : stream given as $b : s$ : $D : U = (b + s) : (b - s)$ , and the times over one distance are in the inverse ratio.
Distances covered in the same time are in the ratio $D : U$ too.
Fast route: keep the ratio parts as plain numbers and scale once at the end with the one real distance, time or speed given.

Boat to stream from the two times

\frac{b}{s} = \frac{t_U + t_D}{t_U - t_D}

$t_U$ time upstream over a distance
$t_D$ time downstream over the same distance

Worked example

A boat takes 9 hours to go upstream between two piers and 5 hours to come back down. Find the ratio of the boat's speed to the stream's speed.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 17 Sep 2024, Shift 2 · Q62Easy

Example 2 · Time, Speed and Distance · Boats and Streams

A motorboat takes 18 hours to go downstream, and it takes 36 hours to return the same distance. Find the ratio of the speed of the boat in still water to the speed of the stream.

Putting the time ratio straight in as the speed ratio

Over the same distance the longer time belongs to the slower, upstream, speed. Upstream and downstream times of 8 and 5 hours mean upstream and downstream speeds in the ratio 5 : 8.

Drill 3 more on boat and stream speeds from a ratio

Concept 3 of 3: Two journeys with two unknown speeds

When two different trips each give a total time, you have two equations in the two speeds. Written with 1 ÷ speed as the unknowns they become straight-line equations, solved by making one coefficient match.

Definition

Let $x = \frac{1}{U}$ and $y = \frac{1}{D}$ . A trip of $a$ km up and $c$ km down in $T$ hours is $ax + cy = T$ .
Multiply one or both equations so that the up distances (or the down distances) match, then subtract to find the other unknown.
Turn $x$ and $y$ back into speeds, then take half the sum and half the difference for the boat and the stream.
Up and back in a total time $T$ over $d$ km gives $x + y = \frac{T}{d}$ at once.
Fast route: speeds that divide the distances exactly are a strong hint. Try them, then check both trips before you choose.

Worked example

A boat goes 30 km upstream and 28 km downstream in 7 hours, and 18 km upstream and 70 km downstream in 8 hours. Find the speeds of the boat in still water and of the stream.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 18 Sep 2024, Shift 1 · Q69Moderate

Example 3 · Time, Speed and Distance · Boats and Streams

A motorboat travelling at some speed can cover 24 km upstream and 40 km downstream in 17 hours. At the same speed it can travel 32 km downstream and 12 km upstream in 10 hours. The speed of the stream is:

Taking the speeds themselves as the unknowns

An equation such as 36 ÷ U + 20 ÷ D = 8 is not a straight-line equation in U and D. Take 1 ÷ U and 1 ÷ D as the unknowns and it is.

Stopping at the downstream and upstream speeds

These questions usually ask for the boat's speed or the stream's speed. After finding D and U, one more step remains: half their sum or half their difference.

Drill 5 more on two journeys with two unknown speeds

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Downstream and upstream speeds
Boats and streams
$D = b + s \qquad U = b - s \qquad b = \frac{D + U}{2} \qquad s = \frac{D - U}{2}$
Boat and stream speeds from a ratio
Boat to stream from the two times
$\frac{b}{s} = \frac{t_U + t_D}{t_U - t_D}$

Watch out for (5)

Forgetting to halve
→ Downstream and upstream speeds
Giving the downstream speed as the boat's speed
→ Downstream and upstream speeds
Putting the time ratio straight in as the speed ratio
→ Boat and stream speeds from a ratio
Taking the speeds themselves as the unknowns
→ Two journeys with two unknown speeds
Stopping at the downstream and upstream speeds
→ Two journeys with two unknown speeds

Test yourself on Time, Speed and Distance

20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Time, Speed and Distance chapter test Drill all 23 questions