CDS Mathematics · Time, Speed and Distance

Boats and Streams

Downstream speed is boat + stream, upstream is boat − stream; the boat's speed is their average and the stream's is half their difference.

All Time, Speed and Distance notes CDS Mathematics strategy

Why this matters

Seven PYQs, all EASY or MODERATE. Find the downstream and upstream speeds first; everything else is an average or half a difference. Round trips and 'equal times' questions become one equation in the stream's speed.

Concept 1 of 1: Downstream and upstream

The current adds to the boat's speed going down and subtracts going up. So the two speeds sit symmetrically around the boat's own speed, the stream's speed away on each side.

Definition

Downstream $d = b + s$ , upstream $u = b - s$ .
$b = \dfrac{d + u}{2}$ , $s = \dfrac{d - u}{2}$ , and $b : s = (d + u) : (d - u)$ .
Round trip of distance $D$ each way in total time $T$ : $\dfrac{D}{b + s} + \dfrac{D}{b - s} = T$ , so $D = \dfrac{T(b^2 - s^2)}{2b}$ .
Equal times for distances $p$ down and $q$ up: $\dfrac{b + s}{b - s} = \dfrac pq$ .

Boat and stream

b = \dfrac{d + u}{2}, \qquad s = \dfrac{d - u}{2}

Worked example

A boat goes

24

km downstream in

2

hours and

16

km upstream in

4

hours. Find the speeds of the boat and the stream.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2021 · CDS (II) 2021 — Elementary Mathematics · Q33Moderate

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

A motor boat has speed 30 km/hr in still water. It goes 60 km down stream and comes back in

\frac{9}{2}

hours. What is the speed of the stream ?

Half the difference, not the difference

Downstream

10

and upstream

2

km/hr give a stream of

4

km/hr, not

8

. The difference

d - u

is TWICE the stream's speed.

Drill 6 more on downstream and upstream

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 (1)

Downstream and upstream
Boat and stream
$b = \dfrac{d + u}{2}, \qquad s = \dfrac{d - u}{2}$

Watch out for (1)

Half the difference, not the difference
→ Downstream and upstream

Test yourself on Time, Speed and Distance

20 past CDS questions from this chapter, timed at 24 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 7 questions